diff --git a/Library/Homebrew/cmd/install.rb b/Library/Homebrew/cmd/install.rb
index 24bf1287b4..99dc96c56a 100644
--- a/Library/Homebrew/cmd/install.rb
+++ b/Library/Homebrew/cmd/install.rb
@@ -15,10 +15,8 @@ require "upgrade"
 module Homebrew
   extend T::Sig
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def install_args
+  def self.install_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Install a <formula> or <cask>. Additional options specific to a <formula> may be
@@ -146,7 +144,7 @@ module Homebrew
     end
   end
 
-  def install
+  def self.install
     args = install_args.parse
 
     if args.env.present?
diff --git a/Library/Homebrew/cmd/reinstall.rb b/Library/Homebrew/cmd/reinstall.rb
index dc09ab35ec..507dbb61d6 100644
--- a/Library/Homebrew/cmd/reinstall.rb
+++ b/Library/Homebrew/cmd/reinstall.rb
@@ -18,10 +18,8 @@ require "api"
 module Homebrew
   extend T::Sig
 
-  module_function
-
   sig { returns(CLI::Parser) }
-  def reinstall_args
+  def self.reinstall_args
     Homebrew::CLI::Parser.new do
       description <<~EOS
         Uninstall and then reinstall a <formula> or <cask> using the same options it was
@@ -92,7 +90,7 @@ module Homebrew
     end
   end
 
-  def reinstall
+  def self.reinstall
     args = reinstall_args.parse
 
     formulae, casks = args.named.to_formulae_and_casks(method: :resolve)
diff --git a/Library/Homebrew/commands.rb b/Library/Homebrew/commands.rb
index 6b0de992a4..993490144e 100644
--- a/Library/Homebrew/commands.rb
+++ b/Library/Homebrew/commands.rb
@@ -7,8 +7,6 @@ require "completions"
 #
 # @api private
 module Commands
-  module_function
-
   HOMEBREW_CMD_PATH = (HOMEBREW_LIBRARY_PATH/"cmd").freeze
   HOMEBREW_DEV_CMD_PATH = (HOMEBREW_LIBRARY_PATH/"dev-cmd").freeze
   # If you are going to change anything in below hash,
@@ -38,35 +36,35 @@ module Commands
   # middle due to dots in URLs or paths.
   DESCRIPTION_SPLITTING_PATTERN = /\.(?>\s|$)/.freeze
 
-  def valid_internal_cmd?(cmd)
+  def self.valid_internal_cmd?(cmd)
     require?(HOMEBREW_CMD_PATH/cmd)
   end
 
-  def valid_internal_dev_cmd?(cmd)
+  def self.valid_internal_dev_cmd?(cmd)
     require?(HOMEBREW_DEV_CMD_PATH/cmd)
   end
 
-  def method_name(cmd)
+  def self.method_name(cmd)
     cmd.to_s
        .tr("-", "_")
        .downcase
        .to_sym
   end
 
-  def args_method_name(cmd_path)
+  def self.args_method_name(cmd_path)
     cmd_path_basename = basename_without_extension(cmd_path)
     cmd_method_prefix = method_name(cmd_path_basename)
     "#{cmd_method_prefix}_args".to_sym
   end
 
-  def internal_cmd_path(cmd)
+  def self.internal_cmd_path(cmd)
     [
       HOMEBREW_CMD_PATH/"#{cmd}.rb",
       HOMEBREW_CMD_PATH/"#{cmd}.sh",
     ].find(&:exist?)
   end
 
-  def internal_dev_cmd_path(cmd)
+  def self.internal_dev_cmd_path(cmd)
     [
       HOMEBREW_DEV_CMD_PATH/"#{cmd}.rb",
       HOMEBREW_DEV_CMD_PATH/"#{cmd}.sh",
@@ -74,21 +72,21 @@ module Commands
   end
 
   # Ruby commands which can be `require`d without being run.
-  def external_ruby_v2_cmd_path(cmd)
+  def self.external_ruby_v2_cmd_path(cmd)
     path = which("#{cmd}.rb", Tap.cmd_directories)
     path if require?(path)
   end
 
   # Ruby commands which are run by being `require`d.
-  def external_ruby_cmd_path(cmd)
+  def self.external_ruby_cmd_path(cmd)
     which("brew-#{cmd}.rb", PATH.new(ENV.fetch("PATH")).append(Tap.cmd_directories))
   end
 
-  def external_cmd_path(cmd)
+  def self.external_cmd_path(cmd)
     which("brew-#{cmd}", PATH.new(ENV.fetch("PATH")).append(Tap.cmd_directories))
   end
 
-  def path(cmd)
+  def self.path(cmd)
     internal_cmd = HOMEBREW_INTERNAL_COMMAND_ALIASES.fetch(cmd, cmd)
     path ||= internal_cmd_path(internal_cmd)
     path ||= internal_dev_cmd_path(internal_cmd)
@@ -98,7 +96,7 @@ module Commands
     path
   end
 
-  def commands(external: true, aliases: false)
+  def self.commands(external: true, aliases: false)
     cmds = internal_commands
     cmds += internal_developer_commands
     cmds += external_commands if external
@@ -106,15 +104,15 @@ module Commands
     cmds.sort
   end
 
-  def internal_commands_paths
+  def self.internal_commands_paths
     find_commands HOMEBREW_CMD_PATH
   end
 
-  def internal_developer_commands_paths
+  def self.internal_developer_commands_paths
     find_commands HOMEBREW_DEV_CMD_PATH
   end
 
-  def official_external_commands_paths(quiet:)
+  def self.official_external_commands_paths(quiet:)
     OFFICIAL_CMD_TAPS.flat_map do |tap_name, cmds|
       tap = Tap.fetch(tap_name)
       tap.install(quiet: quiet) unless tap.installed?
@@ -122,24 +120,24 @@ module Commands
     end
   end
 
-  def internal_commands
+  def self.internal_commands
     find_internal_commands(HOMEBREW_CMD_PATH).map(&:to_s)
   end
 
-  def internal_developer_commands
+  def self.internal_developer_commands
     find_internal_commands(HOMEBREW_DEV_CMD_PATH).map(&:to_s)
   end
 
-  def internal_commands_aliases
+  def self.internal_commands_aliases
     HOMEBREW_INTERNAL_COMMAND_ALIASES.keys
   end
 
-  def find_internal_commands(path)
+  def self.find_internal_commands(path)
     find_commands(path).map(&:basename)
                        .map(&method(:basename_without_extension))
   end
 
-  def external_commands
+  def self.external_commands
     Tap.cmd_directories.flat_map do |path|
       find_commands(path).select(&:executable?)
                          .map(&method(:basename_without_extension))
@@ -148,17 +146,17 @@ module Commands
        .sort
   end
 
-  def basename_without_extension(path)
+  def self.basename_without_extension(path)
     path.basename(path.extname)
   end
 
-  def find_commands(path)
+  def self.find_commands(path)
     Pathname.glob("#{path}/*")
             .select(&:file?)
             .sort
   end
 
-  def rebuild_internal_commands_completion_list
+  def self.rebuild_internal_commands_completion_list
     cmds = internal_commands + internal_developer_commands + internal_commands_aliases
     cmds.reject! { |cmd| Homebrew::Completions::COMPLETIONS_EXCLUSION_LIST.include? cmd }
 
@@ -166,7 +164,7 @@ module Commands
     file.atomic_write("#{cmds.sort.join("\n")}\n")
   end
 
-  def rebuild_commands_completion_list
+  def self.rebuild_commands_completion_list
     # Ensure that the cache exists so we can build the commands list
     HOMEBREW_CACHE.mkpath
 
@@ -178,7 +176,7 @@ module Commands
     external_commands_file.atomic_write("#{external_commands.sort.join("\n")}\n")
   end
 
-  def command_options(command)
+  def self.command_options(command)
     path = self.path(command)
     return if path.blank?
 
@@ -202,7 +200,7 @@ module Commands
     end
   end
 
-  def command_description(command, short: false)
+  def self.command_description(command, short: false)
     path = self.path(command)
     return if path.blank?
 
@@ -228,7 +226,7 @@ module Commands
     end
   end
 
-  def named_args_type(command)
+  def self.named_args_type(command)
     path = self.path(command)
     return if path.blank?
 
@@ -239,7 +237,7 @@ module Commands
   end
 
   # Returns the conflicts of a given `option` for `command`.
-  def option_conflicts(command, option)
+  def self.option_conflicts(command, option)
     path = self.path(command)
     return if path.blank?
 
diff --git a/Library/Homebrew/commands.rbi b/Library/Homebrew/commands.rbi
deleted file mode 100644
index 13522bd09f..0000000000
--- a/Library/Homebrew/commands.rbi
+++ /dev/null
@@ -1,5 +0,0 @@
-# typed: strict
-
-module Commands
-  include Kernel
-end
diff --git a/Library/Homebrew/completions.rb b/Library/Homebrew/completions.rb
index e7fca41fc7..e928a5b837 100644
--- a/Library/Homebrew/completions.rb
+++ b/Library/Homebrew/completions.rb
@@ -20,8 +20,6 @@ module Homebrew
       keyword_init: true,
     )
 
-    module_function
-
     COMPLETIONS_DIR = (HOMEBREW_REPOSITORY/"completions").freeze
     TEMPLATE_DIR = (HOMEBREW_LIBRARY_PATH/"completions").freeze
 
@@ -74,7 +72,7 @@ module Homebrew
     }.freeze
 
     sig { void }
-    def link!
+    def self.link!
       Settings.write :linkcompletions, true
       Tap.each do |tap|
         Utils::Link.link_completions tap.path, "brew completions link"
@@ -82,7 +80,7 @@ module Homebrew
     end
 
     sig { void }
-    def unlink!
+    def self.unlink!
       Settings.write :linkcompletions, false
       Tap.each do |tap|
         next if tap.official?
@@ -92,12 +90,12 @@ module Homebrew
     end
 
     sig { returns(T::Boolean) }
-    def link_completions?
+    def self.link_completions?
       Settings.read(:linkcompletions) == "true"
     end
 
     sig { returns(T::Boolean) }
-    def completions_to_link?
+    def self.completions_to_link?
       Tap.each do |tap|
         next if tap.official?
 
@@ -110,7 +108,7 @@ module Homebrew
     end
 
     sig { void }
-    def show_completions_message_if_needed
+    def self.show_completions_message_if_needed
       return if Settings.read(:completionsmessageshown) == "true"
       return unless completions_to_link?
 
@@ -125,7 +123,7 @@ module Homebrew
     end
 
     sig { void }
-    def update_shell_completions!
+    def self.update_shell_completions!
       commands = Commands.commands(external: false, aliases: true).sort
 
       puts "Writing completions to #{COMPLETIONS_DIR}"
@@ -136,12 +134,12 @@ module Homebrew
     end
 
     sig { params(command: String).returns(T::Boolean) }
-    def command_gets_completions?(command)
+    def self.command_gets_completions?(command)
       command_options(command).any?
     end
 
     sig { params(description: String, fish: T::Boolean).returns(String) }
-    def format_description(description, fish: false)
+    def self.format_description(description, fish: false)
       description = if fish
         description.gsub("'", "\\\\'")
       else
@@ -151,7 +149,7 @@ module Homebrew
     end
 
     sig { params(command: String).returns(T::Hash[String, String]) }
-    def command_options(command)
+    def self.command_options(command)
       options = {}
       Commands.command_options(command)&.each do |option|
         next if option.blank?
@@ -169,7 +167,7 @@ module Homebrew
     end
 
     sig { params(command: String).returns(T.nilable(String)) }
-    def generate_bash_subcommand_completion(command)
+    def self.generate_bash_subcommand_completion(command)
       return unless command_gets_completions? command
 
       named_completion_string = ""
@@ -202,7 +200,7 @@ module Homebrew
     end
 
     sig { params(commands: T::Array[String]).returns(String) }
-    def generate_bash_completion_file(commands)
+    def self.generate_bash_completion_file(commands)
       variables = Variables.new(
         completion_functions: commands.map do |command|
           generate_bash_subcommand_completion command
@@ -218,7 +216,7 @@ module Homebrew
     end
 
     sig { params(command: String).returns(T.nilable(String)) }
-    def generate_zsh_subcommand_completion(command)
+    def self.generate_zsh_subcommand_completion(command)
       return unless command_gets_completions? command
 
       options = command_options(command)
@@ -270,7 +268,7 @@ module Homebrew
       COMPLETION
     end
 
-    def generate_zsh_option_exclusions(command, option)
+    def self.generate_zsh_option_exclusions(command, option)
       conflicts = Commands.option_conflicts(command, option.gsub(/^--/, ""))
       return "" unless conflicts.presence
 
@@ -278,7 +276,7 @@ module Homebrew
     end
 
     sig { params(commands: T::Array[String]).returns(String) }
-    def generate_zsh_completion_file(commands)
+    def self.generate_zsh_completion_file(commands)
       variables = Variables.new(
         aliases:                      Commands::HOMEBREW_INTERNAL_COMMAND_ALIASES.map do |alias_command, command|
           alias_command = "'#{alias_command}'" if alias_command.start_with? "-"
@@ -305,7 +303,7 @@ module Homebrew
     end
 
     sig { params(command: String).returns(T.nilable(String)) }
-    def generate_fish_subcommand_completion(command)
+    def self.generate_fish_subcommand_completion(command)
       return unless command_gets_completions? command
 
       command_description = format_description Commands.command_description(command, short: true), fish: true
@@ -352,7 +350,7 @@ module Homebrew
     end
 
     sig { params(commands: T::Array[String]).returns(String) }
-    def generate_fish_completion_file(commands)
+    def self.generate_fish_completion_file(commands)
       variables = Variables.new(
         completion_functions: commands.map do |command|
           generate_fish_subcommand_completion command
diff --git a/Library/Homebrew/completions.rbi b/Library/Homebrew/completions.rbi
deleted file mode 100644
index 8c4746bcaf..0000000000
--- a/Library/Homebrew/completions.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Homebrew
-  module Completions
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/extend/os/linux/install.rb b/Library/Homebrew/extend/os/linux/install.rb
index 2202386424..cc8a6b4715 100644
--- a/Library/Homebrew/extend/os/linux/install.rb
+++ b/Library/Homebrew/extend/os/linux/install.rb
@@ -3,8 +3,6 @@
 
 module Homebrew
   module Install
-    module_function
-
     # This is a list of known paths to the host dynamic linker on Linux if
     # the host glibc is new enough.  The symlink_ld_so method will fail if
     # the host linker cannot be found in this list.
@@ -32,19 +30,19 @@ module Homebrew
     ].freeze
     private_constant :GCC_RUNTIME_LIBS
 
-    def perform_preinstall_checks(all_fatal: false, cc: nil)
+    def self.perform_preinstall_checks(all_fatal: false, cc: nil)
       generic_perform_preinstall_checks(all_fatal: all_fatal, cc: cc)
       symlink_ld_so
       setup_preferred_gcc_libs
     end
 
-    def global_post_install
+    def self.global_post_install
       generic_global_post_install
       symlink_ld_so
       setup_preferred_gcc_libs
     end
 
-    def check_cpu
+    def self.check_cpu
       return if Hardware::CPU.intel? && Hardware::CPU.is_64_bit?
       return if Hardware::CPU.arm?
 
@@ -59,7 +57,7 @@ module Homebrew
     end
     private_class_method :check_cpu
 
-    def symlink_ld_so
+    def self.symlink_ld_so
       brew_ld_so = HOMEBREW_PREFIX/"lib/ld.so"
 
       ld_so = HOMEBREW_PREFIX/"opt/glibc/bin/ld.so"
@@ -79,7 +77,7 @@ module Homebrew
     end
     private_class_method :symlink_ld_so
 
-    def setup_preferred_gcc_libs
+    def self.setup_preferred_gcc_libs
       gcc_opt_prefix = HOMEBREW_PREFIX/"opt/#{OS::LINUX_PREFERRED_GCC_RUNTIME_FORMULA}"
       glibc_installed = (HOMEBREW_PREFIX/"opt/glibc/bin/ld.so").readable?
 
diff --git a/Library/Homebrew/help.rb b/Library/Homebrew/help.rb
index fba154d8e0..a90d5a2d49 100644
--- a/Library/Homebrew/help.rb
+++ b/Library/Homebrew/help.rb
@@ -41,9 +41,7 @@ module Homebrew
     EOS
     private_constant :HOMEBREW_HELP
 
-    module_function
-
-    def help(cmd = nil, empty_argv: false, usage_error: nil, remaining_args: [])
+    def self.help(cmd = nil, empty_argv: false, usage_error: nil, remaining_args: [])
       if cmd.nil?
         # Handle `brew` (no arguments).
         if empty_argv
@@ -75,7 +73,7 @@ module Homebrew
       exit 0
     end
 
-    def command_help(cmd, path, remaining_args:)
+    def self.command_help(cmd, path, remaining_args:)
       # Only some types of commands can have a parser.
       output = if Commands.valid_internal_cmd?(cmd) ||
                   Commands.valid_internal_dev_cmd?(cmd) ||
@@ -94,7 +92,7 @@ module Homebrew
     end
     private_class_method :command_help
 
-    def parser_help(path, remaining_args:)
+    def self.parser_help(path, remaining_args:)
       # Let OptionParser generate help text for commands which have a parser.
       cmd_parser = CLI::Parser.from_cmd_path(path)
       return unless cmd_parser
@@ -105,7 +103,7 @@ module Homebrew
     end
     private_class_method :parser_help
 
-    def command_help_lines(path)
+    def self.command_help_lines(path)
       path.read
           .lines
           .grep(/^#:/)
@@ -113,7 +111,7 @@ module Homebrew
     end
     private_class_method :command_help_lines
 
-    def comment_help(path)
+    def self.comment_help(path)
       # Otherwise read #: lines from the file.
       help_lines = command_help_lines(path)
       return if help_lines.blank?
diff --git a/Library/Homebrew/help.rbi b/Library/Homebrew/help.rbi
deleted file mode 100644
index 9db873c525..0000000000
--- a/Library/Homebrew/help.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Homebrew
-  module Help
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/install.rb b/Library/Homebrew/install.rb
index fdf31bbe8a..49ace9b935 100644
--- a/Library/Homebrew/install.rb
+++ b/Library/Homebrew/install.rb
@@ -12,8 +12,7 @@ module Homebrew
   #
   # @api private
   module Install
-    module_function
-
+    class << self
     def perform_preinstall_checks(all_fatal: false, cc: nil)
       check_prefix
       check_cpu
@@ -23,7 +22,6 @@ module Homebrew
       Diagnostic.checks(:fatal_preinstall_checks)
     end
     alias generic_perform_preinstall_checks perform_preinstall_checks
-    module_function :generic_perform_preinstall_checks
 
     def perform_build_from_source_checks(all_fatal: false)
       Diagnostic.checks(:fatal_build_from_source_checks)
@@ -32,7 +30,6 @@ module Homebrew
 
     def global_post_install; end
     alias generic_global_post_install global_post_install
-    module_function :generic_global_post_install
 
     def check_prefix
       if (Hardware::CPU.intel? || Hardware::CPU.in_rosetta2?) &&
@@ -364,5 +361,6 @@ module Homebrew
     end
   end
 end
+end
 
 require "extend/os/install"
diff --git a/Library/Homebrew/install.rbi b/Library/Homebrew/install.rbi
deleted file mode 100644
index 5208127284..0000000000
--- a/Library/Homebrew/install.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Homebrew
-  module Install
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/language/perl.rb b/Library/Homebrew/language/perl.rb
index f4822239ad..3aea71dbf5 100644
--- a/Library/Homebrew/language/perl.rb
+++ b/Library/Homebrew/language/perl.rb
@@ -8,9 +8,7 @@ module Language
   module Perl
     # Helper module for replacing `perl` shebangs.
     module Shebang
-      module_function
-
-      def detected_perl_shebang(formula = self)
+      def self.detected_perl_shebang(formula = self)
         perl_path = if formula.deps.map(&:name).include? "perl"
           Formula["perl"].opt_bin/"perl"
         elsif formula.uses_from_macos_names.include? "perl"
diff --git a/Library/Homebrew/language/perl.rbi b/Library/Homebrew/language/perl.rbi
deleted file mode 100644
index 9be98f1896..0000000000
--- a/Library/Homebrew/language/perl.rbi
+++ /dev/null
@@ -1,9 +0,0 @@
-# typed: strict
-
-module Language
-  module Perl
-    module Shebang
-      include Kernel
-    end
-  end
-end
diff --git a/Library/Homebrew/language/python.rb b/Library/Homebrew/language/python.rb
index b8d890e840..a5082f2f90 100644
--- a/Library/Homebrew/language/python.rb
+++ b/Library/Homebrew/language/python.rb
@@ -92,10 +92,8 @@ module Language
 
     # Mixin module for {Formula} adding shebang rewrite features.
     module Shebang
-      module_function
-
       # @private
-      def python_shebang_rewrite_info(python_path)
+      def self.python_shebang_rewrite_info(python_path)
         Utils::Shebang::RewriteInfo.new(
           %r{^#! ?/usr/bin/(?:env )?python(?:[23](?:\.\d{1,2})?)?( |$)},
           28, # the length of "#! /usr/bin/env pythonx.yyy "
@@ -103,7 +101,7 @@ module Language
         )
       end
 
-      def detected_python_shebang(formula = self, use_python_from_path: false)
+      def self.detected_python_shebang(formula = self, use_python_from_path: false)
         python_path = if use_python_from_path
           "/usr/bin/env python3"
         else
diff --git a/Library/Homebrew/language/python.rbi b/Library/Homebrew/language/python.rbi
index ab011b8db7..ad9e51f69d 100644
--- a/Library/Homebrew/language/python.rbi
+++ b/Library/Homebrew/language/python.rbi
@@ -1,11 +1,5 @@
 # typed: strict
 
-module Language::Python
-  module Shebang
-    include Kernel
-  end
-
-  module Virtualenv
-    requires_ancestor { Formula }
-  end
+module Language::Python::Virtualenv
+  requires_ancestor { Formula }
 end
diff --git a/Library/Homebrew/manpages.rb b/Library/Homebrew/manpages.rb
index 42b91bc3ac..3787ef826e 100644
--- a/Library/Homebrew/manpages.rb
+++ b/Library/Homebrew/manpages.rb
@@ -29,9 +29,7 @@ module Homebrew
       keyword_init: true,
     )
 
-    module_function
-
-    def regenerate_man_pages(quiet:)
+    def self.regenerate_man_pages(quiet:)
       Homebrew.install_bundler_gems!
 
       markup = build_man_page(quiet: quiet)
@@ -39,7 +37,7 @@ module Homebrew
       convert_man_page(markup, TARGET_MAN_PATH/"brew.1")
     end
 
-    def build_man_page(quiet:)
+    def self.build_man_page(quiet:)
       template = (SOURCE_PATH/"brew.1.md.erb").read
       readme = HOMEBREW_REPOSITORY/"README.md"
       variables = Variables.new(
@@ -64,12 +62,12 @@ module Homebrew
       ERB.new(template, trim_mode: ">").result(variables.instance_eval { binding })
     end
 
-    def sort_key_for_path(path)
+    def self.sort_key_for_path(path)
       # Options after regular commands (`~` comes after `z` in ASCII table).
       path.basename.to_s.sub(/\.(rb|sh)$/, "").sub(/^--/, "~~")
     end
 
-    def convert_man_page(markup, target)
+    def self.convert_man_page(markup, target)
       manual = target.basename(".1")
       organisation = "Homebrew"
 
@@ -113,7 +111,7 @@ module Homebrew
       end
     end
 
-    def target_path_to_format(target)
+    def self.target_path_to_format(target)
       case target.basename
       when /\.md$/    then ["--markdown", "markdown"]
       when /\.\d$/    then ["--roff", "man page"]
@@ -122,7 +120,7 @@ module Homebrew
       end
     end
 
-    def generate_cmd_manpages(cmd_paths)
+    def self.generate_cmd_manpages(cmd_paths)
       man_page_lines = []
 
       # preserve existing manpage order
@@ -142,7 +140,7 @@ module Homebrew
       man_page_lines.compact.join("\n")
     end
 
-    def cmd_parser_manpage_lines(cmd_parser)
+    def self.cmd_parser_manpage_lines(cmd_parser)
       lines = [format_usage_banner(cmd_parser.usage_banner_text)]
       lines += cmd_parser.processed_options.map do |short, long, _, desc, hidden|
         next if hidden
@@ -159,7 +157,7 @@ module Homebrew
       lines
     end
 
-    def cmd_comment_manpage_lines(cmd_path)
+    def self.cmd_comment_manpage_lines(cmd_path)
       comment_lines = cmd_path.read.lines.grep(/^#:/)
       return if comment_lines.empty?
       return if comment_lines.first.include?("@hide_from_man_page")
@@ -185,7 +183,7 @@ module Homebrew
     end
 
     sig { returns(String) }
-    def global_cask_options_manpage
+    def self.global_cask_options_manpage
       lines = ["These options are applicable to the `install`, `reinstall`, and `upgrade` " \
                "subcommands with the `--cask` flag.\n"]
       lines += Homebrew::CLI::Parser.global_cask_options.map do |_, long, description:, **|
@@ -195,7 +193,7 @@ module Homebrew
     end
 
     sig { returns(String) }
-    def global_options_manpage
+    def self.global_options_manpage
       lines = ["These options are applicable across multiple subcommands.\n"]
       lines += Homebrew::CLI::Parser.global_options.map do |short, long, desc|
         generate_option_doc(short, long, desc)
@@ -204,7 +202,7 @@ module Homebrew
     end
 
     sig { returns(String) }
-    def env_vars_manpage
+    def self.env_vars_manpage
       lines = Homebrew::EnvConfig::ENVS.flat_map do |env, hash|
         entry = "- `#{env}`:\n  <br>#{hash[:description]}\n"
         default = hash[:default_text]
@@ -216,11 +214,11 @@ module Homebrew
       lines.join("\n")
     end
 
-    def format_opt(opt)
+    def self.format_opt(opt)
       "`#{opt}`" unless opt.nil?
     end
 
-    def generate_option_doc(short, long, desc)
+    def self.generate_option_doc(short, long, desc)
       comma = (short && long) ? ", " : ""
       <<~EOS
         * #{format_opt(short)}#{comma}#{format_opt(long)}:
@@ -228,7 +226,7 @@ module Homebrew
       EOS
     end
 
-    def format_usage_banner(usage_banner)
+    def self.format_usage_banner(usage_banner)
       usage_banner&.sub(/^(#: *\* )?/, "### ")
     end
   end
diff --git a/Library/Homebrew/manpages.rbi b/Library/Homebrew/manpages.rbi
deleted file mode 100644
index d3765f73a3..0000000000
--- a/Library/Homebrew/manpages.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Homebrew
-  module Manpages
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/os/linux.rb b/Library/Homebrew/os/linux.rb
index 2b5df8cfc3..cf03b80ada 100644
--- a/Library/Homebrew/os/linux.rb
+++ b/Library/Homebrew/os/linux.rb
@@ -8,10 +8,8 @@ module OS
   module Linux
     extend T::Sig
 
-    module_function
-
     sig { returns(String) }
-    def os_version
+    def self.os_version
       if which("lsb_release")
         lsb_info = Utils.popen_read("lsb_release", "-a")
         description = lsb_info[/^Description:\s*(.*)$/, 1].force_encoding("UTF-8")
@@ -29,12 +27,12 @@ module OS
     end
 
     sig { returns(T::Boolean) }
-    def wsl?
+    def self.wsl?
       /-microsoft/i.match?(OS.kernel_version.to_s)
     end
 
     sig { returns(Version) }
-    def wsl_version
+    def self.wsl_version
       return Version::NULL unless wsl?
 
       kernel = OS.kernel_version.to_s
@@ -58,42 +56,42 @@ module OS
 
     raise "Loaded OS::Linux on generic OS!" if ENV["HOMEBREW_TEST_GENERIC_OS"]
 
-    def version
+    def self.version
       ::Version::NULL
     end
 
-    def full_version
+    def self.full_version
       ::Version::NULL
     end
 
-    def languages
+    def self.languages
       @languages ||= Array(ENV["LANG"]&.slice(/[a-z]+/)).uniq
     end
 
-    def language
+    def self.language
       languages.first
     end
 
-    def sdk_root_needed?
+    def self.sdk_root_needed?
       false
     end
 
-    def sdk_path_if_needed(_version = nil)
+    def self.sdk_path_if_needed(_version = nil)
       nil
     end
 
-    def sdk_path(_version = nil)
+    def self.sdk_path(_version = nil)
       nil
     end
 
     module Xcode
       module_function
 
-      def version
+      def self.version
         ::Version::NULL
       end
 
-      def installed?
+      def self.installed?
         false
       end
     end
@@ -101,11 +99,11 @@ module OS
     module CLT
       module_function
 
-      def version
+      def self.version
         ::Version::NULL
       end
 
-      def installed?
+      def self.installed?
         false
       end
     end
diff --git a/Library/Homebrew/os/linux.rbi b/Library/Homebrew/os/linux.rbi
deleted file mode 100644
index b6f3164683..0000000000
--- a/Library/Homebrew/os/linux.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module OS
-  module Linux
-    include ::Kernel
-  end
-end
diff --git a/Library/Homebrew/os/mac.rb b/Library/Homebrew/os/mac.rb
index b52a965130..4b6eeffe23 100644
--- a/Library/Homebrew/os/mac.rb
+++ b/Library/Homebrew/os/mac.rb
@@ -11,8 +11,6 @@ module OS
   module Mac
     extend T::Sig
 
-    module_function
-
     ::MacOS = OS::Mac
 
     raise "Loaded OS::Mac on generic OS!" if ENV["HOMEBREW_TEST_GENERIC_OS"]
@@ -23,14 +21,14 @@ module OS
     # This can be compared to numerics, strings, or symbols
     # using the standard Ruby Comparable methods.
     sig { returns(Version) }
-    def version
+    def self.version
       @version ||= full_version.strip_patch
     end
 
     # This can be compared to numerics, strings, or symbols
     # using the standard Ruby Comparable methods.
     sig { returns(Version) }
-    def full_version
+    def self.full_version
       @full_version ||= if ENV["HOMEBREW_FAKE_EL_CAPITAN"] # for Portable Ruby building
         Version.new("10.11.6")
       else
@@ -39,21 +37,20 @@ module OS
     end
 
     sig { params(version: String).void }
-    def full_version=(version)
+    def self.full_version=(version)
       @full_version = Version.new(version.chomp)
       @version = nil
     end
 
     sig { returns(::Version) }
-    def latest_sdk_version
+    def self.latest_sdk_version
       # TODO: bump version when new Xcode macOS SDK is released
       # NOTE: We only track the major version of the SDK.
       ::Version.new("13")
     end
-    private :latest_sdk_version
 
     sig { returns(String) }
-    def preferred_perl_version
+    def self.preferred_perl_version
       if version >= :big_sur
         "5.30"
       else
@@ -61,7 +58,7 @@ module OS
       end
     end
 
-    def languages
+    def self.languages
       return @languages if @languages
 
       os_langs = Utils.popen_read("defaults", "read", "-g", "AppleLanguages")
@@ -74,17 +71,17 @@ module OS
       @languages = os_langs
     end
 
-    def language
+    def self.language
       languages.first
     end
 
     sig { returns(String) }
-    def active_developer_dir
+    def self.active_developer_dir
       @active_developer_dir ||= Utils.popen_read("/usr/bin/xcode-select", "-print-path").strip
     end
 
     sig { returns(T::Boolean) }
-    def sdk_root_needed?
+    def self.sdk_root_needed?
       if MacOS::CLT.installed?
         # If there's no CLT SDK, return false
         return false unless MacOS::CLT.provides_sdk?
@@ -105,7 +102,7 @@ module OS
     # If no specific SDK is requested, the SDK matching the OS version is returned,
     # if available. Otherwise, the latest SDK is returned.
 
-    def sdk_locator
+    def self.sdk_locator
       if CLT.installed? && CLT.provides_sdk?
         CLT.sdk_locator
       else
@@ -113,11 +110,11 @@ module OS
       end
     end
 
-    def sdk(version = nil)
+    def self.sdk(version = nil)
       sdk_locator.sdk_if_applicable(version)
     end
 
-    def sdk_for_formula(formula, version = nil, check_only_runtime_requirements: false)
+    def self.sdk_for_formula(formula, version = nil, check_only_runtime_requirements: false)
       # If the formula requires Xcode, don't return the CLT SDK
       # If check_only_runtime_requirements is true, don't necessarily return the
       # Xcode SDK if the XcodeRequirement is only a build or test requirement.
@@ -132,12 +129,12 @@ module OS
     end
 
     # Returns the path to an SDK or nil, following the rules set by {sdk}.
-    def sdk_path(version = nil)
+    def self.sdk_path(version = nil)
       s = sdk(version)
       s&.path
     end
 
-    def sdk_path_if_needed(version = nil)
+    def self.sdk_path_if_needed(version = nil)
       # Prefer CLT SDK when both Xcode and the CLT are installed.
       # Expected results:
       # 1. On Xcode-only systems, return the Xcode SDK.
@@ -156,7 +153,7 @@ module OS
     # - {https://github.com/Homebrew/legacy-homebrew/issues/13}
     # - {https://github.com/Homebrew/legacy-homebrew/issues/41}
     # - {https://github.com/Homebrew/legacy-homebrew/issues/48}
-    def macports_or_fink
+    def self.macports_or_fink
       paths = []
 
       # First look in the path because MacPorts is relocatable and Fink
@@ -186,7 +183,7 @@ module OS
     end
 
     sig { params(ids: String).returns(T.nilable(Pathname)) }
-    def app_with_bundle_id(*ids)
+    def self.app_with_bundle_id(*ids)
       path = mdfind(*ids)
              .reject { |p| p.include?("/Backups.backupdb/") }
              .first
@@ -194,20 +191,20 @@ module OS
     end
 
     sig { params(ids: String).returns(T::Array[String]) }
-    def mdfind(*ids)
+    def self.mdfind(*ids)
       (@mdfind ||= {}).fetch(ids) do
         @mdfind[ids] = Utils.popen_read("/usr/bin/mdfind", mdfind_query(*ids)).split("\n")
       end
     end
 
-    def pkgutil_info(id)
+    def self.pkgutil_info(id)
       (@pkginfo ||= {}).fetch(id) do |key|
         @pkginfo[key] = Utils.popen_read("/usr/sbin/pkgutil", "--pkg-info", key).strip
       end
     end
 
     sig { params(ids: String).returns(String) }
-    def mdfind_query(*ids)
+    def self.mdfind_query(*ids)
       ids.map! { |id| "kMDItemCFBundleIdentifier == #{id}" }.join(" || ")
     end
   end
diff --git a/Library/Homebrew/os/mac.rbi b/Library/Homebrew/os/mac.rbi
deleted file mode 100644
index 85a546f554..0000000000
--- a/Library/Homebrew/os/mac.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module OS
-  module Mac
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/os/mac/xcode.rb b/Library/Homebrew/os/mac/xcode.rb
index 6e234f8268..70f610e63e 100755
--- a/Library/Homebrew/os/mac/xcode.rb
+++ b/Library/Homebrew/os/mac/xcode.rb
@@ -9,8 +9,6 @@ module OS
     module Xcode
       extend T::Sig
 
-      module_function
-
       DEFAULT_BUNDLE_PATH = Pathname("/Applications/Xcode.app").freeze
       BUNDLE_ID = "com.apple.dt.Xcode"
       OLD_BUNDLE_ID = "com.apple.Xcode"
@@ -20,7 +18,7 @@ module OS
       # CI systems have been updated.
       # This may be a beta version for a beta macOS.
       sig { params(macos: MacOS::Version).returns(String) }
-      def latest_version(macos: MacOS.version)
+      def self.latest_version(macos: MacOS.version)
         latest_stable = "14.3"
         case macos
         when "13" then latest_stable
@@ -44,7 +42,7 @@ module OS
       # macOS version (which may initially be a beta if that version of macOS is
       # also in beta).
       sig { returns(String) }
-      def minimum_version
+      def self.minimum_version
         case MacOS.version
         when "13" then "14.1"
         when "12" then "13.1"
@@ -58,19 +56,19 @@ module OS
       end
 
       sig { returns(T::Boolean) }
-      def below_minimum_version?
+      def self.below_minimum_version?
         return false unless installed?
 
         version < minimum_version
       end
 
       sig { returns(T::Boolean) }
-      def latest_sdk_version?
+      def self.latest_sdk_version?
         OS::Mac.full_version >= OS::Mac.latest_sdk_version
       end
 
       sig { returns(T::Boolean) }
-      def needs_clt_installed?
+      def self.needs_clt_installed?
         return false if latest_sdk_version?
 
         # With fake El Capitan for Portable Ruby, we want the full 10.11 SDK so that we can link
@@ -82,21 +80,21 @@ module OS
       end
 
       sig { returns(T::Boolean) }
-      def outdated?
+      def self.outdated?
         return false unless installed?
 
         version < latest_version
       end
 
       sig { returns(T::Boolean) }
-      def without_clt?
+      def self.without_clt?
         !MacOS::CLT.installed?
       end
 
       # Returns a Pathname object corresponding to Xcode.app's Developer
       # directory or nil if Xcode.app is not installed.
       sig { returns(T.nilable(Pathname)) }
-      def prefix
+      def self.prefix
         return @prefix if defined?(@prefix)
 
         @prefix = T.let(@prefix, T.nilable(Pathname))
@@ -115,12 +113,12 @@ module OS
       end
 
       sig { returns(Pathname) }
-      def toolchain_path
+      def self.toolchain_path
         Pathname("#{prefix}/Toolchains/XcodeDefault.xctoolchain")
       end
 
       sig { returns(T.nilable(Pathname)) }
-      def bundle_path
+      def self.bundle_path
         # Use the default location if it exists.
         return DEFAULT_BUNDLE_PATH if DEFAULT_BUNDLE_PATH.exist?
 
@@ -131,27 +129,27 @@ module OS
       end
 
       sig { returns(T::Boolean) }
-      def installed?
+      def self.installed?
         !prefix.nil?
       end
 
       sig { returns(XcodeSDKLocator) }
-      def sdk_locator
+      def self.sdk_locator
         @sdk_locator ||= XcodeSDKLocator.new
       end
 
       sig { params(version: T.nilable(MacOS::Version)).returns(T.nilable(SDK)) }
-      def sdk(version = nil)
+      def self.sdk(version = nil)
         sdk_locator.sdk_if_applicable(version)
       end
 
       sig { params(version: T.nilable(MacOS::Version)).returns(T.nilable(Pathname)) }
-      def sdk_path(version = nil)
+      def self.sdk_path(version = nil)
         sdk(version)&.path
       end
 
       sig { returns(String) }
-      def installation_instructions
+      def self.installation_instructions
         if OS::Mac.version.prerelease?
           <<~EOS
             Xcode can be installed from:
@@ -165,7 +163,7 @@ module OS
       end
 
       sig { returns(String) }
-      def update_instructions
+      def self.update_instructions
         if OS::Mac.version.prerelease?
           <<~EOS
             Xcode can be updated from:
@@ -179,7 +177,7 @@ module OS
       end
 
       sig { returns(::Version) }
-      def version
+      def self.version
         # may return a version string
         # that is guessed based on the compiler, so do not
         # use it in order to check if Xcode is installed.
@@ -191,7 +189,7 @@ module OS
       end
 
       sig { returns(T.nilable(String)) }
-      def detect_version
+      def self.detect_version
         # This is a separate function as you can't cache the value out of a block
         # if return is used in the middle, which we do many times in here.
         return if !MacOS::Xcode.installed? && !MacOS::CLT.installed?
@@ -219,7 +217,7 @@ module OS
       end
 
       sig { returns(String) }
-      def detect_version_from_clang_version
+      def self.detect_version_from_clang_version
         version = DevelopmentTools.clang_version
 
         return "dunno" if version.null?
@@ -252,7 +250,7 @@ module OS
       end
 
       sig { returns(T::Boolean) }
-      def default_prefix?
+      def self.default_prefix?
         prefix.to_s == "/Applications/Xcode.app/Contents/Developer"
       end
     end
@@ -272,37 +270,37 @@ module OS
 
       # Returns true even if outdated tools are installed.
       sig { returns(T::Boolean) }
-      def installed?
+      def self.installed?
         !version.null?
       end
 
       sig { returns(T::Boolean) }
-      def separate_header_package?
+      def self.separate_header_package?
         version >= "10" && MacOS.version >= "10.14"
       end
 
       sig { returns(T::Boolean) }
-      def provides_sdk?
+      def self.provides_sdk?
         version >= "8"
       end
 
       sig { returns(CLTSDKLocator) }
-      def sdk_locator
+      def self.sdk_locator
         @sdk_locator ||= CLTSDKLocator.new
       end
 
       sig { params(version: T.nilable(MacOS::Version)).returns(T.nilable(SDK)) }
-      def sdk(version = nil)
+      def self.sdk(version = nil)
         sdk_locator.sdk_if_applicable(version)
       end
 
       sig { params(version: T.nilable(MacOS::Version)).returns(T.nilable(Pathname)) }
-      def sdk_path(version = nil)
+      def self.sdk_path(version = nil)
         sdk(version)&.path
       end
 
       sig { returns(String) }
-      def installation_instructions
+      def self.installation_instructions
         if MacOS.version == "10.14"
           # This is not available from `xcode-select`
           <<~EOS
@@ -318,7 +316,7 @@ module OS
       end
 
       sig { returns(String) }
-      def update_instructions
+      def self.update_instructions
         software_update_location = if MacOS.version >= "13"
           "System Settings"
         elsif MacOS.version >= "10.14"
@@ -343,7 +341,7 @@ module OS
       # Bump these when the new version is distributed through Software Update
       # and our CI systems have been updated.
       sig { returns(String) }
-      def latest_clang_version
+      def self.latest_clang_version
         case MacOS.version
         when "13"    then "1403.0.22.14.1"
         when "12"    then "1400.0.29.202"
@@ -360,7 +358,7 @@ module OS
       # without this. Generally this will be the first stable CLT release on
       # that macOS version.
       sig { returns(String) }
-      def minimum_version
+      def self.minimum_version
         case MacOS.version
         when "13" then "14.0.0"
         when "12" then "13.0.0"
@@ -374,14 +372,14 @@ module OS
       end
 
       sig { returns(T::Boolean) }
-      def below_minimum_version?
+      def self.below_minimum_version?
         return false unless installed?
 
         version < minimum_version
       end
 
       sig { returns(T::Boolean) }
-      def outdated?
+      def self.outdated?
         clang_version = detect_clang_version
         return false unless clang_version
 
@@ -389,13 +387,13 @@ module OS
       end
 
       sig { returns(T.nilable(String)) }
-      def detect_clang_version
+      def self.detect_clang_version
         version_output = Utils.popen_read("#{PKG_PATH}/usr/bin/clang", "--version")
         version_output[/clang-(\d+(\.\d+)+)/, 1]
       end
 
       sig { returns(T.nilable(String)) }
-      def detect_version_from_clang_version
+      def self.detect_version_from_clang_version
         detect_clang_version&.sub(/^(\d+)0(\d)\./, "\\1.\\2.")
       end
 
@@ -403,7 +401,7 @@ module OS
       # Note that the different ways of installing the CLTs lead to different
       # version numbers.
       sig { returns(::Version) }
-      def version
+      def self.version
         if @version ||= detect_version
           ::Version.new @version
         else
@@ -412,7 +410,7 @@ module OS
       end
 
       sig { returns(T.nilable(String)) }
-      def detect_version
+      def self.detect_version
         version = T.let(nil, T.nilable(String))
         [EXECUTABLE_PKG_ID, MAVERICKS_NEW_PKG_ID].each do |id|
           next unless File.exist?("#{PKG_PATH}/usr/bin/clang")
diff --git a/Library/Homebrew/os/mac/xcode.rbi b/Library/Homebrew/os/mac/xcode.rbi
deleted file mode 100644
index b0707a034e..0000000000
--- a/Library/Homebrew/os/mac/xcode.rbi
+++ /dev/null
@@ -1,9 +0,0 @@
-# typed: strict
-
-module OS
-  module Mac
-    module Xcode
-      include Kernel
-    end
-  end
-end
diff --git a/Library/Homebrew/search.rb b/Library/Homebrew/search.rb
index 94175561a2..14f8d15f01 100644
--- a/Library/Homebrew/search.rb
+++ b/Library/Homebrew/search.rb
@@ -8,9 +8,7 @@ module Homebrew
   #
   # @api private
   module Search
-    module_function
-
-    def query_regexp(query)
+    def self.query_regexp(query)
       if (m = query.match(%r{^/(.*)/$}))
         Regexp.new(m[1])
       else
@@ -20,7 +18,7 @@ module Homebrew
       raise "#{query} is not a valid regex."
     end
 
-    def search_descriptions(string_or_regex, args, search_type: :desc)
+    def self.search_descriptions(string_or_regex, args, search_type: :desc)
       both = !args.formula? && !args.cask?
       eval_all = args.eval_all? || Homebrew::EnvConfig.eval_all?
 
@@ -42,7 +40,7 @@ module Homebrew
       end
     end
 
-    def search_formulae(string_or_regex)
+    def self.search_formulae(string_or_regex)
       if string_or_regex.is_a?(String) && string_or_regex.match?(HOMEBREW_TAP_FORMULA_REGEX)
         return begin
           [Formulary.factory(string_or_regex).name]
@@ -74,7 +72,7 @@ module Homebrew
       end.compact
     end
 
-    def search_casks(string_or_regex)
+    def self.search_casks(string_or_regex)
       if string_or_regex.is_a?(String) && string_or_regex.match?(HOMEBREW_TAP_CASK_REGEX)
         return begin
           [Cask::CaskLoader.load(string_or_regex).token]
@@ -104,7 +102,7 @@ module Homebrew
       end.uniq
     end
 
-    def search_names(string_or_regex, args)
+    def self.search_names(string_or_regex, args)
       both = !args.formula? && !args.cask?
 
       all_formulae = if args.formula? || both
@@ -122,7 +120,7 @@ module Homebrew
       [all_formulae, all_casks]
     end
 
-    def search(selectable, string_or_regex, &block)
+    def self.search(selectable, string_or_regex, &block)
       case string_or_regex
       when Regexp
         search_regex(selectable, string_or_regex, &block)
@@ -131,11 +129,11 @@ module Homebrew
       end
     end
 
-    def simplify_string(string)
+    def self.simplify_string(string)
       string.downcase.gsub(/[^a-z\d]/i, "")
     end
 
-    def search_regex(selectable, regex)
+    def self.search_regex(selectable, regex)
       selectable.select do |*args|
         args = yield(*args) if block_given?
         args = Array(args).flatten.compact
@@ -143,7 +141,7 @@ module Homebrew
       end
     end
 
-    def search_string(selectable, string)
+    def self.search_string(selectable, string)
       simplified_string = simplify_string(string)
       selectable.select do |*args|
         args = yield(*args) if block_given?
diff --git a/Library/Homebrew/search.rbi b/Library/Homebrew/search.rbi
deleted file mode 100644
index 2c8f4bdb6e..0000000000
--- a/Library/Homebrew/search.rbi
+++ /dev/null
@@ -1,5 +0,0 @@
-# typed: strict
-
-module Homebrew::Search
-  include Kernel
-end
diff --git a/Library/Homebrew/settings.rb b/Library/Homebrew/settings.rb
index f04820eef2..4e5914899d 100644
--- a/Library/Homebrew/settings.rb
+++ b/Library/Homebrew/settings.rb
@@ -8,9 +8,7 @@ module Homebrew
   #
   # @api private
   module Settings
-    module_function
-
-    def read(setting, repo: HOMEBREW_REPOSITORY)
+    def self.read(setting, repo: HOMEBREW_REPOSITORY)
       return unless (repo/".git/config").exist?
 
       value = Utils.popen_read("git", "-C", repo.to_s, "config", "--get", "homebrew.#{setting}").chomp
@@ -20,7 +18,7 @@ module Homebrew
       value
     end
 
-    def write(setting, value, repo: HOMEBREW_REPOSITORY)
+    def self.write(setting, value, repo: HOMEBREW_REPOSITORY)
       return unless (repo/".git/config").exist?
 
       value = value.to_s
@@ -30,7 +28,7 @@ module Homebrew
       Kernel.system("git", "-C", repo.to_s, "config", "--replace-all", "homebrew.#{setting}", value, exception: true)
     end
 
-    def delete(setting, repo: HOMEBREW_REPOSITORY)
+    def self.delete(setting, repo: HOMEBREW_REPOSITORY)
       return unless (repo/".git/config").exist?
 
       return if read(setting, repo: repo).blank?
diff --git a/Library/Homebrew/settings.rbi b/Library/Homebrew/settings.rbi
deleted file mode 100644
index d902c06acb..0000000000
--- a/Library/Homebrew/settings.rbi
+++ /dev/null
@@ -1,16 +0,0 @@
-# typed: strict
-
-module Homebrew
-  module Settings
-    include Kernel
-
-    sig { params(setting: T.any(String, Symbol), repo: Pathname).returns(T.nilable(String)) }
-    def read(setting, repo: HOMEBREW_REPOSITORY); end
-
-    sig { params(setting: T.any(String, Symbol), value: T.any(String, T::Boolean), repo: Pathname).void }
-    def write(setting, value, repo: HOMEBREW_REPOSITORY); end
-
-    sig { params(setting: T.any(String, Symbol), repo: Pathname).void }
-    def delete(setting, repo: HOMEBREW_REPOSITORY); end
-  end
-end
diff --git a/Library/Homebrew/uninstall.rb b/Library/Homebrew/uninstall.rb
index a6f366f448..73578c5ce2 100644
--- a/Library/Homebrew/uninstall.rb
+++ b/Library/Homebrew/uninstall.rb
@@ -8,9 +8,7 @@ module Homebrew
   #
   # @api private
   module Uninstall
-    module_function
-
-    def uninstall_kegs(kegs_by_rack, casks: [], force: false, ignore_dependencies: false, named_args: [])
+    def self.uninstall_kegs(kegs_by_rack, casks: [], force: false, ignore_dependencies: false, named_args: [])
       handle_unsatisfied_dependents(kegs_by_rack,
                                     casks:               casks,
                                     ignore_dependencies: ignore_dependencies,
@@ -97,7 +95,7 @@ module Homebrew
       end
     end
 
-    def handle_unsatisfied_dependents(kegs_by_rack, casks: [], ignore_dependencies: false, named_args: [])
+    def self.handle_unsatisfied_dependents(kegs_by_rack, casks: [], ignore_dependencies: false, named_args: [])
       return if ignore_dependencies
 
       all_kegs = kegs_by_rack.values.flatten(1)
@@ -107,7 +105,7 @@ module Homebrew
       nil
     end
 
-    def check_for_dependents(kegs, casks: [], named_args: [])
+    def self.check_for_dependents(kegs, casks: [], named_args: [])
       return false unless (result = InstalledDependents.find_some_installed_dependents(kegs, casks: casks))
 
       if Homebrew::EnvConfig.developer?
@@ -164,7 +162,7 @@ module Homebrew
       end
     end
 
-    def rm_pin(rack)
+    def self.rm_pin(rack)
       Formulary.from_rack(rack).unpin
     rescue
       nil
diff --git a/Library/Homebrew/uninstall.rbi b/Library/Homebrew/uninstall.rbi
deleted file mode 100644
index f801c23a87..0000000000
--- a/Library/Homebrew/uninstall.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Homebrew
-  module Uninstall
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/utils/formatter.rb b/Library/Homebrew/utils/formatter.rb
index 870364c142..33b8909ea3 100644
--- a/Library/Homebrew/utils/formatter.rb
+++ b/Library/Homebrew/utils/formatter.rb
@@ -7,33 +7,31 @@ require "utils/tty"
 #
 # @api private
 module Formatter
-  module_function
-
-  def arrow(string, color: nil)
+  def self.arrow(string, color: nil)
     prefix("==>", string, color)
   end
 
-  def headline(string, color: nil)
+  def self.headline(string, color: nil)
     arrow("#{Tty.bold}#{string}#{Tty.reset}", color: color)
   end
 
-  def identifier(string)
+  def self.identifier(string)
     "#{Tty.green}#{string}#{Tty.default}"
   end
 
-  def option(string)
+  def self.option(string)
     "#{Tty.bold}#{string}#{Tty.reset}"
   end
 
-  def success(string, label: nil)
+  def self.success(string, label: nil)
     label(label, string, :green)
   end
 
-  def warning(string, label: nil)
+  def self.warning(string, label: nil)
     label(label, string, :yellow)
   end
 
-  def error(string, label: nil)
+  def self.error(string, label: nil)
     label(label, string, :red)
   end
 
@@ -50,7 +48,7 @@ module Formatter
   # so we always wrap one word before an option.
   # @see https://github.com/Homebrew/brew/pull/12672
   # @see https://macromates.com/blog/2006/wrapping-text-with-regular-expressions/
-  def format_help_text(string, width: 172)
+  def self.format_help_text(string, width: 172)
     desc = OPTION_DESC_WIDTH
     indent = width - desc
     string.gsub(/(?<=\S) *\n(?=\S)/, " ")
@@ -60,17 +58,17 @@ module Formatter
           .gsub(/(.{1,#{width}})( +|$)(?!-)\n?/, "\\1\n")
   end
 
-  def url(string)
+  def self.url(string)
     "#{Tty.underline}#{string}#{Tty.no_underline}"
   end
 
-  def label(label, string, color)
+  def self.label(label, string, color)
     label = "#{label}:" unless label.nil?
     prefix(label, string, color)
   end
   private_class_method :label
 
-  def prefix(prefix, string, color)
+  def self.prefix(prefix, string, color)
     if prefix.nil? && color.nil?
       string
     elsif prefix.nil?
@@ -83,7 +81,7 @@ module Formatter
   end
   private_class_method :prefix
 
-  def columns(*objects, gap_size: 2)
+  def self.columns(*objects, gap_size: 2)
     objects = objects.flatten.map(&:to_s)
 
     fallback = proc do
diff --git a/Library/Homebrew/utils/formatter.rbi b/Library/Homebrew/utils/formatter.rbi
deleted file mode 100644
index e9038dd0f3..0000000000
--- a/Library/Homebrew/utils/formatter.rbi
+++ /dev/null
@@ -1,5 +0,0 @@
-# typed: strict
-
-module Formatter
-  include Kernel
-end
diff --git a/Library/Homebrew/utils/github/api.rb b/Library/Homebrew/utils/github/api.rb
index 0d122975a9..9155b86797 100644
--- a/Library/Homebrew/utils/github/api.rb
+++ b/Library/Homebrew/utils/github/api.rb
@@ -33,8 +33,6 @@ module GitHub
   module API
     extend T::Sig
 
-    module_function
-
     # Generic API error.
     class Error < RuntimeError
       attr_reader :github_message
@@ -119,7 +117,7 @@ module GitHub
     # Gets the password field from `git-credential-osxkeychain` for github.com,
     # but only if that password looks like a GitHub Personal Access Token.
     sig { returns(T.nilable(String)) }
-    def keychain_username_password
+    def self.keychain_username_password
       github_credentials = Utils.popen_write("git", "credential-osxkeychain", "get") do |pipe|
         pipe.write "protocol=https\nhost=github.com\n"
       end
@@ -141,12 +139,12 @@ module GitHub
       nil
     end
 
-    def credentials
+    def self.credentials
       @credentials ||= Homebrew::EnvConfig.github_api_token || keychain_username_password
     end
 
     sig { returns(Symbol) }
-    def credentials_type
+    def self.credentials_type
       if Homebrew::EnvConfig.github_api_token
         :env_token
       elsif keychain_username_password
@@ -158,7 +156,7 @@ module GitHub
 
     # Given an API response from GitHub, warn the user if their credentials
     # have insufficient permissions.
-    def credentials_error_message(response_headers, needed_scopes)
+    def self.credentials_error_message(response_headers, needed_scopes)
       return if response_headers.empty?
 
       scopes = response_headers["x-accepted-oauth-scopes"].to_s.split(", ")
@@ -184,7 +182,7 @@ module GitHub
       EOS
     end
 
-    def open_rest(url, data: nil, data_binary_path: nil, request_method: nil, scopes: [].freeze, parse_json: true)
+    def self.open_rest(url, data: nil, data_binary_path: nil, request_method: nil, scopes: [].freeze, parse_json: true)
       # This is a no-op if the user is opting out of using the GitHub API.
       return block_given? ? yield({}) : {} if Homebrew::EnvConfig.no_github_api?
 
@@ -253,7 +251,7 @@ module GitHub
       end
     end
 
-    def paginate_rest(url, additional_query_params: nil, per_page: 100)
+    def self.paginate_rest(url, additional_query_params: nil, per_page: 100)
       (1..API_MAX_PAGES).each do |page|
         result = API.open_rest("#{url}?per_page=#{per_page}&page=#{page}&#{additional_query_params}")
         break if result.blank?
@@ -262,7 +260,7 @@ module GitHub
       end
     end
 
-    def open_graphql(query, variables: nil, scopes: [].freeze, raise_errors: true)
+    def self.open_graphql(query, variables: nil, scopes: [].freeze, raise_errors: true)
       data = { query: query, variables: variables }
       result = open_rest("#{API_URL}/graphql", scopes: scopes, data: data, request_method: "POST")
 
@@ -277,7 +275,7 @@ module GitHub
       end
     end
 
-    def raise_error(output, errors, http_code, headers, scopes)
+    def self.raise_error(output, errors, http_code, headers, scopes)
       json = begin
         JSON.parse(output)
       rescue
diff --git a/Library/Homebrew/utils/github/api.rbi b/Library/Homebrew/utils/github/api.rbi
deleted file mode 100644
index bb72675c19..0000000000
--- a/Library/Homebrew/utils/github/api.rbi
+++ /dev/null
@@ -1,5 +0,0 @@
-# typed: strict
-
-module GitHub::API
-  include Kernel
-end
diff --git a/Library/Homebrew/utils/gzip.rb b/Library/Homebrew/utils/gzip.rb
index b5cbd04fa7..18a649751c 100644
--- a/Library/Homebrew/utils/gzip.rb
+++ b/Library/Homebrew/utils/gzip.rb
@@ -10,8 +10,6 @@ module Utils
   module Gzip
     extend T::Sig
 
-    module_function
-
     sig {
       params(
         path:      T.any(String, Pathname),
@@ -20,7 +18,7 @@ module Utils
         output:    T.any(String, Pathname),
       ).returns(Pathname)
     }
-    def compress_with_options(path, mtime: ENV["SOURCE_DATE_EPOCH"].to_i, orig_name: File.basename(path),
+    def self.compress_with_options(path, mtime: ENV["SOURCE_DATE_EPOCH"].to_i, orig_name: File.basename(path),
                               output: "#{path}.gz")
       # Ideally, we would just set mtime = 0 if SOURCE_DATE_EPOCH is absent, but Ruby's
       # Zlib::GzipWriter does not properly handle the case of setting mtime = 0:
@@ -55,7 +53,7 @@ module Utils
         mtime:        T.any(Integer, Time),
       ).returns(T::Array[Pathname])
     }
-    def compress(*paths, reproducible: true, mtime: ENV["SOURCE_DATE_EPOCH"].to_i)
+    def self.compress(*paths, reproducible: true, mtime: ENV["SOURCE_DATE_EPOCH"].to_i)
       if reproducible
         paths.map do |path|
           compress_with_options(path, mtime: mtime)
diff --git a/Library/Homebrew/utils/gzip.rbi b/Library/Homebrew/utils/gzip.rbi
deleted file mode 100644
index 7b7201eaca..0000000000
--- a/Library/Homebrew/utils/gzip.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Utils
-  module Gzip
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/utils/inreplace.rb b/Library/Homebrew/utils/inreplace.rb
index 50ff78f80b..354b11c8f7 100644
--- a/Library/Homebrew/utils/inreplace.rb
+++ b/Library/Homebrew/utils/inreplace.rb
@@ -20,8 +20,6 @@ module Utils
       end
     end
 
-    module_function
-
     # Sometimes we have to change a bit before we install. Mostly we
     # prefer a patch, but if you need the {Formula#prefix prefix} of
     # this formula in the patch you have to resort to `inreplace`,
@@ -47,7 +45,7 @@ module Utils
         audit_result: T::Boolean,
       ).void
     }
-    def inreplace(paths, before = nil, after = nil, audit_result = true) # rubocop:disable Style/OptionalBooleanParameter
+    def self.inreplace(paths, before = nil, after = nil, audit_result = true) # rubocop:disable Style/OptionalBooleanParameter
       after = after.to_s if after.is_a? Symbol
 
       errors = {}
@@ -73,7 +71,7 @@ module Utils
     end
 
     # @api private
-    def inreplace_pairs(path, replacement_pairs, read_only_run: false, silent: false)
+    def self.inreplace_pairs(path, replacement_pairs, read_only_run: false, silent: false)
       str = File.binread(path)
       contents = StringInreplaceExtension.new(str)
       replacement_pairs.each do |old, new|
diff --git a/Library/Homebrew/utils/inreplace.rbi b/Library/Homebrew/utils/inreplace.rbi
deleted file mode 100644
index 02542091d2..0000000000
--- a/Library/Homebrew/utils/inreplace.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Utils
-  module Inreplace
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/utils/link.rb b/Library/Homebrew/utils/link.rb
index c33d5ca335..d166878bc3 100644
--- a/Library/Homebrew/utils/link.rb
+++ b/Library/Homebrew/utils/link.rb
@@ -6,9 +6,7 @@ module Utils
   #
   # @api private
   module Link
-    module_function
-
-    def link_src_dst_dirs(src_dir, dst_dir, command, link_dir: false)
+    def self.link_src_dst_dirs(src_dir, dst_dir, command, link_dir: false)
       return unless src_dir.exist?
 
       conflicts = []
@@ -42,7 +40,7 @@ module Utils
     end
     private_class_method :link_src_dst_dirs
 
-    def unlink_src_dst_dirs(src_dir, dst_dir, unlink_dir: false)
+    def self.unlink_src_dst_dirs(src_dir, dst_dir, unlink_dir: false)
       return unless src_dir.exist?
 
       src_paths = unlink_dir ? [src_dir] : src_dir.find
@@ -56,27 +54,27 @@ module Utils
     end
     private_class_method :unlink_src_dst_dirs
 
-    def link_manpages(path, command)
+    def self.link_manpages(path, command)
       link_src_dst_dirs(path/"manpages", HOMEBREW_PREFIX/"share/man/man1", command)
     end
 
-    def unlink_manpages(path)
+    def self.unlink_manpages(path)
       unlink_src_dst_dirs(path/"manpages", HOMEBREW_PREFIX/"share/man/man1")
     end
 
-    def link_completions(path, command)
+    def self.link_completions(path, command)
       link_src_dst_dirs(path/"completions/bash", HOMEBREW_PREFIX/"etc/bash_completion.d", command)
       link_src_dst_dirs(path/"completions/zsh", HOMEBREW_PREFIX/"share/zsh/site-functions", command)
       link_src_dst_dirs(path/"completions/fish", HOMEBREW_PREFIX/"share/fish/vendor_completions.d", command)
     end
 
-    def unlink_completions(path)
+    def self.unlink_completions(path)
       unlink_src_dst_dirs(path/"completions/bash", HOMEBREW_PREFIX/"etc/bash_completion.d")
       unlink_src_dst_dirs(path/"completions/zsh", HOMEBREW_PREFIX/"share/zsh/site-functions")
       unlink_src_dst_dirs(path/"completions/fish", HOMEBREW_PREFIX/"share/fish/vendor_completions.d")
     end
 
-    def link_docs(path, command)
+    def self.link_docs(path, command)
       link_src_dst_dirs(path/"docs", HOMEBREW_PREFIX/"share/doc/homebrew", command, link_dir: true)
     end
   end
diff --git a/Library/Homebrew/utils/link.rbi b/Library/Homebrew/utils/link.rbi
deleted file mode 100644
index 0b88a48d16..0000000000
--- a/Library/Homebrew/utils/link.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Utils
-  module Link
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/utils/repology.rb b/Library/Homebrew/utils/repology.rb
index dc9fc61cec..b40a05cc03 100644
--- a/Library/Homebrew/utils/repology.rb
+++ b/Library/Homebrew/utils/repology.rb
@@ -9,13 +9,10 @@ require "utils/curl"
 module Repology
   HOMEBREW_CORE = "homebrew"
   HOMEBREW_CASK = "homebrew_casks"
-
-  module_function
-
   MAX_PAGINATION = 15
   private_constant :MAX_PAGINATION
 
-  def query_api(last_package_in_response = "", repository:)
+  def self.query_api(last_package_in_response = "", repository:)
     last_package_in_response += "/" if last_package_in_response.present?
     url = "https://repology.org/api/v1/projects/#{last_package_in_response}?inrepo=#{repository}&outdated=1"
 
@@ -31,7 +28,7 @@ module Repology
     raise
   end
 
-  def single_package_query(name, repository:)
+  def self.single_package_query(name, repository:)
     url = "https://repology.org/tools/project-by?repo=#{repository}&" \
           "name_type=srcname&target_page=api_v1_project&name=#{name}"
 
@@ -50,7 +47,7 @@ module Repology
     nil
   end
 
-  def parse_api_response(limit = nil, last_package = "", repository:)
+  def self.parse_api_response(limit = nil, last_package = "", repository:)
     package_term = case repository
     when HOMEBREW_CORE
       "formulae"
@@ -83,7 +80,7 @@ module Repology
     outdated_packages.sort.to_h
   end
 
-  def latest_version(repositories)
+  def self.latest_version(repositories)
     # The status is "unique" when the package is present only in Homebrew, so
     # Repology has no way of knowing if the package is up-to-date.
     is_unique = repositories.find do |repo|
diff --git a/Library/Homebrew/utils/repology.rbi b/Library/Homebrew/utils/repology.rbi
deleted file mode 100644
index 57ed1c467f..0000000000
--- a/Library/Homebrew/utils/repology.rbi
+++ /dev/null
@@ -1,6 +0,0 @@
-# typed: strict
-
-module Repology
-  include Kernel
-  requires_ancestor { Utils::Curl }
-end
diff --git a/Library/Homebrew/utils/shebang.rb b/Library/Homebrew/utils/shebang.rb
index edf36e0f0c..22cf7f2c62 100644
--- a/Library/Homebrew/utils/shebang.rb
+++ b/Library/Homebrew/utils/shebang.rb
@@ -8,8 +8,6 @@ module Utils
   module Shebang
     extend T::Sig
 
-    module_function
-
     # Specification on how to rewrite a given shebang.
     #
     # @api private
@@ -33,7 +31,7 @@ module Utils
     #
     # @api public
     sig { params(rewrite_info: RewriteInfo, paths: T::Array[T.any(String, Pathname)]).void }
-    def rewrite_shebang(rewrite_info, *paths)
+    def self.rewrite_shebang(rewrite_info, *paths)
       paths.each do |f|
         f = Pathname(f)
         next unless f.file?
diff --git a/Library/Homebrew/utils/shebang.rbi b/Library/Homebrew/utils/shebang.rbi
deleted file mode 100644
index 9cdb0b2007..0000000000
--- a/Library/Homebrew/utils/shebang.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Utils
-  module Shebang
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/utils/shell.rb b/Library/Homebrew/utils/shell.rb
index 4fe444be02..c27dac0562 100644
--- a/Library/Homebrew/utils/shell.rb
+++ b/Library/Homebrew/utils/shell.rb
@@ -5,12 +5,10 @@ module Utils
   module Shell
     extend T::Sig
 
-    module_function
-
     # Take a path and heuristically convert it to a shell name,
     # return `nil` if there's no match.
     sig { params(path: String).returns(T.nilable(Symbol)) }
-    def from_path(path)
+    def self.from_path(path)
       # we only care about the basename
       shell_name = File.basename(path)
       # handle possible version suffix like `zsh-5.2`
@@ -19,23 +17,23 @@ module Utils
     end
 
     sig { params(default: String).returns(String) }
-    def preferred_path(default: "")
+    def self.preferred_path(default: "")
       ENV.fetch("SHELL", default)
     end
 
     sig { returns(T.nilable(Symbol)) }
-    def preferred
+    def self.preferred
       from_path(preferred_path)
     end
 
     sig { returns(T.nilable(Symbol)) }
-    def parent
+    def self.parent
       from_path(`ps -p #{Process.ppid} -o ucomm=`.strip)
     end
 
     # Quote values. Quoting keys is overkill.
     sig { params(key: String, value: String, shell: T.nilable(Symbol)).returns(T.nilable(String)) }
-    def export_value(key, value, shell = preferred)
+    def self.export_value(key, value, shell = preferred)
       case shell
       when :bash, :ksh, :mksh, :sh, :zsh
         "export #{key}=\"#{sh_quote(value)}\""
@@ -51,7 +49,7 @@ module Utils
 
     # Return the shell profile file based on user's preferred shell.
     sig { returns(String) }
-    def profile
+    def self.profile
       case preferred
       when :bash
         bash_profile = "#{Dir.home}/.bash_profile"
@@ -64,7 +62,7 @@ module Utils
     end
 
     sig { params(variable: String, value: String).returns(T.nilable(String)) }
-    def set_variable_in_profile(variable, value)
+    def self.set_variable_in_profile(variable, value)
       case preferred
       when :bash, :ksh, :sh, :zsh, nil
         "echo 'export #{variable}=#{sh_quote(value)}' >> #{profile}"
@@ -76,7 +74,7 @@ module Utils
     end
 
     sig { params(path: String).returns(T.nilable(String)) }
-    def prepend_path_in_profile(path)
+    def self.prepend_path_in_profile(path)
       case preferred
       when :bash, :ksh, :mksh, :sh, :zsh, nil
         "echo 'export PATH=\"#{sh_quote(path)}:$PATH\"' >> #{profile}"
@@ -101,7 +99,7 @@ module Utils
     UNSAFE_SHELL_CHAR = %r{([^A-Za-z0-9_\-.,:/@~\n])}.freeze
 
     sig { params(str: String).returns(String) }
-    def csh_quote(str)
+    def self.csh_quote(str)
       # ruby's implementation of shell_escape
       str = str.to_s
       return "''" if str.empty?
@@ -115,7 +113,7 @@ module Utils
     end
 
     sig { params(str: String).returns(String) }
-    def sh_quote(str)
+    def self.sh_quote(str)
       # ruby's implementation of shell_escape
       str = str.to_s
       return "''" if str.empty?
diff --git a/Library/Homebrew/utils/shell.rbi b/Library/Homebrew/utils/shell.rbi
deleted file mode 100644
index b860bc1190..0000000000
--- a/Library/Homebrew/utils/shell.rbi
+++ /dev/null
@@ -1,7 +0,0 @@
-# typed: strict
-
-module Utils
-  module Shell
-    include Kernel
-  end
-end
diff --git a/Library/Homebrew/warnings.rb b/Library/Homebrew/warnings.rb
index f0a3ed116f..28387659a8 100644
--- a/Library/Homebrew/warnings.rb
+++ b/Library/Homebrew/warnings.rb
@@ -7,8 +7,6 @@ require "warning"
 #
 # @api private
 module Warnings
-  module_function
-
   COMMON_WARNINGS = {
     parser_syntax: [
       %r{warning: parser/current is loading parser/ruby\d+, which recognizes},
@@ -17,7 +15,7 @@ module Warnings
     ],
   }.freeze
 
-  def ignore(*warnings)
+  def self.ignore(*warnings)
     warnings.map! do |warning|
       next warning if !warning.is_a?(Symbol) || !COMMON_WARNINGS.key?(warning)
 
diff --git a/Library/Homebrew/warnings.rbi b/Library/Homebrew/warnings.rbi
deleted file mode 100644
index 5d83b4cc35..0000000000
--- a/Library/Homebrew/warnings.rbi
+++ /dev/null
@@ -1,5 +0,0 @@
-# typed: strict
-
-module Warnings
-  include Kernel
-end