diff --git a/Library/Homebrew/diagnostic.rb b/Library/Homebrew/diagnostic.rb
index b1a788ba37..0c2e7b2935 100644
--- a/Library/Homebrew/diagnostic.rb
+++ b/Library/Homebrew/diagnostic.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "keg"
@@ -16,7 +16,12 @@ require "system_command"
 module Homebrew
   # Module containing diagnostic checks.
   module Diagnostic
-    def self.missing_deps(formulae, hide = [])
+    sig {
+      params(formulae: T::Array[Formula], hide: T::Array[String], _block: T.nilable(
+        T.proc.params(formula_name: String, missing_dependencies: T::Array[Formula]).void,
+      )).returns(T::Hash[String, T::Array[String]])
+    }
+    def self.missing_deps(formulae, hide = [], &_block)
       missing = {}
       formulae.each do |f|
         missing_dependencies = f.missing_dependencies(hide: hide)
@@ -28,8 +33,9 @@ module Homebrew
       missing
     end
 
+    sig { params(type: Symbol, fatal: T::Boolean).void }
     def self.checks(type, fatal: true)
-      @checks ||= Checks.new
+      @checks ||= T.let(Checks.new, T.nilable(Checks))
       failed = T.let(false, T::Boolean)
       @checks.public_send(type).each do |check|
         out = @checks.public_send(check)
@@ -49,14 +55,21 @@ module Homebrew
     class Checks
       include SystemCommand::Mixin
 
+      sig { params(verbose: T::Boolean).void }
       def initialize(verbose: true)
-        @verbose = verbose
+        @verbose = T.let(verbose, T::Boolean)
+        @found = T.let([], T::Array[String])
+        @seen_prefix_bin = T.let(false, T::Boolean)
+        @seen_prefix_sbin = T.let(false, T::Boolean)
+        @user_path_1_done = T.let(false, T::Boolean)
+        @non_core_taps = T.let([], T.nilable(T::Array[Tap]))
       end
 
       ############# @!group HELPERS
       # Finds files in `HOMEBREW_PREFIX` *and* /usr/local.
       # Specify paths relative to a prefix, e.g. "include/foo.h".
       # Sets @found for your convenience.
+      sig { params(relative_paths: T.any(String, T::Array[String])).void }
       def find_relative_paths(*relative_paths)
         @found = [HOMEBREW_PREFIX, "/usr/local"].uniq.reduce([]) do |found, prefix|
           found + relative_paths.map { |f| File.join(prefix, f) }.select { |f| File.exist? f }
@@ -69,44 +82,52 @@ module Homebrew
             .freeze
       end
 
+      sig { params(path: String).returns(String) }
       def user_tilde(path)
         path.gsub(Dir.home, "~")
       end
 
-      sig { returns(String) }
+      sig { returns(T.nilable(String)) }
       def none_string
         "<NONE>"
       end
 
+      sig { params(args: T.anything).returns(T.nilable(String)) }
       def add_info(*args)
         ohai(*args) if @verbose
       end
       ############# @!endgroup END HELPERS
 
+      sig { returns(T::Array[String]) }
       def fatal_preinstall_checks
         %w[
           check_access_directories
         ].freeze
       end
 
+      sig { returns(T::Array[String]) }
       def fatal_build_from_source_checks
         %w[
           check_for_installed_developer_tools
         ].freeze
       end
 
+      sig { returns(T::Array[String]) }
       def fatal_setup_build_environment_checks
         [].freeze
       end
 
+      sig { returns(T::Array[String]) }
       def supported_configuration_checks
         [].freeze
       end
 
+      sig { returns(T::Array[String]) }
       def build_from_source_checks
         [].freeze
       end
 
+      sig { returns(T::Array[String]) }
       def build_error_checks
         supported_configuration_checks + build_from_source_checks
       end
@@ -156,6 +177,7 @@ module Homebrew
         end
       end
 
+      sig { params(tap: Tap).returns(T.nilable(String)) }
       def broken_tap(tap)
         return unless Utils::Git.available?
 
@@ -177,6 +199,7 @@ module Homebrew
         message
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_installed_developer_tools
         return if DevelopmentTools.installed?
 
@@ -186,6 +209,7 @@ module Homebrew
         EOS
       end
 
+      sig { params(dir: String, pattern: String, allow_list: T::Array[String], message: String).returns(T.nilable(String)) }
       def __check_stray_files(dir, pattern, allow_list, message)
         return unless File.directory?(dir)
 
@@ -203,6 +227,7 @@ module Homebrew
         inject_file_list(files, message)
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_stray_dylibs
         # Dylibs which are generally OK should be added to this list,
         # with a short description of the software they come with.
@@ -236,6 +261,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_stray_static_libs
         # Static libs which are generally OK should be added to this list,
         # with a short description of the software they come with.
@@ -261,6 +287,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_stray_pcs
         # Package-config files which are generally OK should be added to this list,
         # with a short description of the software they come with.
@@ -282,6 +309,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_stray_las
         allow_list = [
           "libfuse.la", # MacFuse
@@ -303,6 +331,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_stray_headers
         allow_list = [
           "fuse.h", # MacFuse
@@ -323,6 +352,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_broken_symlinks
         broken_symlinks = []
 
@@ -340,6 +370,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_tmpdir_sticky_bit
         world_writable = HOMEBREW_TEMP.stat.mode & 0777 == 0777
         return if !world_writable || HOMEBREW_TEMP.sticky?
@@ -351,6 +382,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_exist_directories
         return if HOMEBREW_PREFIX.writable?
 
@@ -367,6 +399,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_access_directories
         not_writable_dirs =
           Keg.must_be_writable_directories.select(&:exist?)
@@ -385,6 +418,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_multiple_cellars
         return if HOMEBREW_PREFIX.to_s == HOMEBREW_REPOSITORY.to_s
         return unless (HOMEBREW_REPOSITORY/"Cellar").exist?
@@ -397,6 +431,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_user_path_1
         @seen_prefix_bin = false
         @seen_prefix_sbin = false
@@ -436,8 +471,9 @@ module Homebrew
         message unless message.empty?
       end
 
+      sig { returns(T.nilable(String)) }
       def check_user_path_2
-        check_user_path_1 unless defined?(@user_path_1_done)
+        check_user_path_1 unless @user_path_1_done
         return if @seen_prefix_bin
 
         <<~EOS
@@ -447,8 +483,9 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_user_path_3
-        check_user_path_1 unless defined?(@user_path_1_done)
+        check_user_path_1 unless @user_path_1_done
         return if @seen_prefix_sbin
 
         # Don't complain about sbin not being in the path if it doesn't exist
@@ -465,6 +502,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_symlinked_cellar
         return unless HOMEBREW_CELLAR.exist?
         return unless HOMEBREW_CELLAR.symlink?
@@ -484,6 +522,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_git_version
         minimum_version = ENV.fetch("HOMEBREW_MINIMUM_GIT_VERSION")
         return unless Utils::Git.available?
@@ -499,6 +538,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_git
         return if Utils::Git.available?
 
@@ -510,6 +550,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_git_newline_settings
         return unless Utils::Git.available?
 
@@ -528,11 +569,13 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_brew_git_origin
         repo = GitRepository.new(HOMEBREW_REPOSITORY)
         examine_git_origin(repo, Homebrew::EnvConfig.brew_git_remote)
       end
 
+      sig { returns(T.nilable(String)) }
       def check_coretap_integrity
         core_tap = CoreTap.instance
         unless core_tap.installed?
@@ -544,6 +587,7 @@ module Homebrew
         broken_tap(core_tap) || examine_git_origin(core_tap.git_repository, Homebrew::EnvConfig.core_git_remote)
       end
 
+      sig { returns(T.nilable(String)) }
       def check_casktap_integrity
         core_cask_tap = CoreCaskTap.instance
         return unless core_cask_tap.installed?
@@ -571,6 +615,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_deprecated_official_taps
         tapped_deprecated_taps =
           Tap.select(&:official?).map(&:repository) & DEPRECATED_OFFICIAL_TAPS
@@ -587,6 +632,7 @@ module Homebrew
         EOS
       end
 
+      sig { params(formula: Formula).returns(T::Boolean) }
       def __check_linked_brew!(formula)
         formula.installed_prefixes.each do |prefix|
           prefix.find do |src|
@@ -600,6 +646,7 @@ module Homebrew
         false
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_other_frameworks
         # Other frameworks that are known to cause problems when present
         frameworks_to_check = %w[
@@ -619,6 +666,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_tmpdir
         tmpdir = ENV.fetch("TMPDIR", nil)
         return if tmpdir.nil? || File.directory?(tmpdir)
@@ -628,6 +676,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_missing_deps
         return unless HOMEBREW_CELLAR.exist?
 
@@ -646,6 +695,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_deprecated_disabled
         return unless HOMEBREW_CELLAR.exist?
 
@@ -660,6 +710,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_deprecated_disabled
         deprecated_or_disabled = Cask::Caskroom.casks.select(&:deprecated?)
         deprecated_or_disabled += Cask::Caskroom.casks.select(&:disabled?)
@@ -716,6 +767,7 @@ module Homebrew
         message
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_non_prefixed_coreutils
         coreutils = Formula["coreutils"]
         return unless coreutils.any_version_installed?
@@ -730,6 +782,7 @@ module Homebrew
         nil
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_pydistutils_cfg_in_home
         return unless File.exist? "#{Dir.home}/.pydistutils.cfg"
 
@@ -741,6 +794,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_unreadable_installed_formula
         formula_unavailable_exceptions = []
         Formula.racks.each do |rack|
@@ -759,6 +813,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_unlinked_but_not_keg_only
         unlinked = Formula.racks.reject do |rack|
           next true if (HOMEBREW_LINKED_KEGS/rack.basename).directory?
@@ -778,6 +833,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_external_cmd_name_conflict
         cmds = Commands.tap_cmd_directories.flat_map { |p| Dir["#{p}/brew-*"] }.uniq
         cmds = cmds.select { |cmd| File.file?(cmd) && File.executable?(cmd) }
@@ -805,6 +861,7 @@ module Homebrew
         message
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_tap_ruby_files_locations
         bad_tap_files = {}
         Tap.installed.each do |tap|
@@ -831,6 +888,7 @@ module Homebrew
         end.join("\n")
       end
 
+      sig { returns(T.nilable(String)) }
       def check_homebrew_prefix
         return if Homebrew.default_prefix?
 
@@ -844,6 +902,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_deleted_formula
         kegs = Keg.all
 
@@ -878,6 +937,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_unnecessary_core_tap
         return if Homebrew::EnvConfig.developer?
         return if Homebrew::EnvConfig.no_install_from_api?
@@ -892,6 +952,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_unnecessary_cask_tap
         return if Homebrew::EnvConfig.developer?
         return if Homebrew::EnvConfig.no_install_from_api?
@@ -908,6 +969,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_deprecated_cask_taps
         tapped_caskroom_taps = ::Tap.select { |t| t.user == "caskroom" || t.name == "phinze/cask" }
                                     .map(&:name)
@@ -921,12 +983,14 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_software_versions
         add_info "Homebrew Version", HOMEBREW_VERSION
 
         nil
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_install_location
         locations = Dir.glob(HOMEBREW_CELLAR.join("brew-cask", "*")).reverse
         return if locations.empty?
@@ -936,6 +1000,7 @@ module Homebrew
         end.join "\n"
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_staging_location
         # Skip this check when running CI since the staging path is not writable for security reasons
         return if GitHub::Actions.env_set?
@@ -953,6 +1018,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_taps
         error_tap_paths = []
 
@@ -975,6 +1041,7 @@ module Homebrew
         "Unable to read from cask #{taps_string}: #{error_tap_paths.to_sentence}" if error_tap_paths.present?
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_load_path
         paths = $LOAD_PATH.map { user_tilde(_1) }
 
@@ -983,6 +1050,7 @@ module Homebrew
         "$LOAD_PATH is empty" if paths.blank?
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_environment_variables
         environment_variables = %w[
           RUBYLIB
@@ -1011,6 +1079,7 @@ module Homebrew
         nil
       end
 
+      sig { returns(T.nilable(String)) }
       def check_cask_xattr
         # If quarantine is not available, a warning is already shown by check_cask_quarantine_support so just return
         return unless Cask::Quarantine.available?
@@ -1043,10 +1112,12 @@ module Homebrew
         end
       end
 
+      sig { returns(T::Array[Tap]) }
       def non_core_taps
         @non_core_taps ||= Tap.installed.reject(&:core_tap?).reject(&:core_cask_tap?)
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_duplicate_formulae
         return if ENV["HOMEBREW_TEST_BOT"].present?
 
@@ -1074,6 +1145,7 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T.nilable(String)) }
       def check_for_duplicate_casks
         return if ENV["HOMEBREW_TEST_BOT"].present?
 
@@ -1101,14 +1173,17 @@ module Homebrew
         EOS
       end
 
+      sig { returns(T::Array[String]) }
       def all
         methods.map(&:to_s).grep(/^check_/).sort
       end
 
+      sig { returns(T::Array[String]) }
       def cask_checks
         all.grep(/^check_cask_/)
       end
 
+      sig { returns(String) }
       def current_user
         ENV.fetch("USER", "$(whoami)")
       end
diff --git a/Library/Homebrew/extend/os/linux/diagnostic.rb b/Library/Homebrew/extend/os/linux/diagnostic.rb
index d9e2073996..92e8f03a86 100644
--- a/Library/Homebrew/extend/os/linux/diagnostic.rb
+++ b/Library/Homebrew/extend/os/linux/diagnostic.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:disable Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "tempfile"
@@ -16,6 +16,7 @@ module OS
 
         requires_ancestor { Homebrew::Diagnostic::Checks }
 
+        sig { returns(T::Array[String]) }
         def fatal_preinstall_checks
           %w[
             check_access_directories
@@ -24,6 +25,7 @@ module OS
           ].freeze
         end
 
+        sig { returns(T::Array[String]) }
         def supported_configuration_checks
           %w[
             check_glibc_minimum_version
@@ -32,6 +34,7 @@ module OS
           ].freeze
         end
 
+        sig { returns(T.nilable(String)) }
         def check_tmpdir_sticky_bit
           message = super
           return if message.nil?
@@ -45,6 +48,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_tmpdir_executable
           f = Tempfile.new(%w[homebrew_check_tmpdir_executable .sh], HOMEBREW_TEMP)
           f.write "#!/bin/sh\n"
@@ -63,6 +67,7 @@ module OS
           f&.unlink
         end
 
+        sig { returns(T.nilable(String)) }
         def check_umask_not_zero
           return unless File.umask.zero?
 
@@ -74,6 +79,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_supported_architecture
           return if ::Hardware::CPU.intel?
           return if Homebrew::EnvConfig.developer? && ENV["HOMEBREW_ARM64_TESTING"].present? && ::Hardware::CPU.arm?
@@ -86,6 +92,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_glibc_minimum_version
           return unless OS::Linux::Glibc.below_minimum_version?
 
@@ -101,6 +108,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_glibc_version
           return unless OS::Linux::Glibc.below_ci_version?
 
@@ -119,6 +127,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_kernel_minimum_version
           return unless OS::Linux::Kernel.below_minimum_version?
 
@@ -135,6 +144,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_linuxbrew_core
           return unless Homebrew::EnvConfig.no_install_from_api?
           return unless CoreTap.instance.linuxbrew_core?
@@ -145,6 +155,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_linuxbrew_bottle_domain
           return unless Homebrew::EnvConfig.bottle_domain.include?("linuxbrew")
 
@@ -155,6 +166,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_symlinked_home
           return unless File.symlink?("/home")
 
@@ -176,6 +188,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_gcc_dependent_linkage
           gcc_dependents = ::Formula.installed.select do |formula|
             next false unless formula.tap&.core_tap?
@@ -212,6 +225,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_cask_software_versions
           super
           add_info "Linux", OS::Linux.os_version
diff --git a/Library/Homebrew/extend/os/mac/diagnostic.rb b/Library/Homebrew/extend/os/mac/diagnostic.rb
index 1d563b7694..ced2ce3a8f 100644
--- a/Library/Homebrew/extend/os/mac/diagnostic.rb
+++ b/Library/Homebrew/extend/os/mac/diagnostic.rb
@@ -1,14 +1,16 @@
-# typed: true # rubocop:disable Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 module OS
   module Mac
     module Diagnostic
       class Volumes
+        sig { void }
         def initialize
-          @volumes = get_mounts
+          @volumes = T.let(get_mounts, T::Array[String])
         end
 
+        sig { params(path: T.nilable(Pathname)).returns(Integer) }
         def which(path)
           vols = get_mounts path
 
@@ -22,12 +24,13 @@ module OS
           vol_index
         end
 
+        sig { params(path: T.nilable(Pathname)).returns(T::Array[String]) }
         def get_mounts(path = nil)
           vols = []
           # get the volume of path, if path is nil returns all volumes
 
           args = %w[/bin/df -P]
-          args << path if path
+          args << path.to_s if path
 
           Utils.popen_read(*args) do |io|
             io.each_line do |line|
@@ -47,6 +50,13 @@ module OS
 
         requires_ancestor { Homebrew::Diagnostic::Checks }
 
+        sig { params(verbose: T::Boolean).void }
+        def initialize(verbose: true)
+          super
+          @found = T.let([], T::Array[String])
+        end
+
+        sig { returns(T::Array[String]) }
         def fatal_preinstall_checks
           checks = %w[
             check_access_directories
@@ -58,6 +68,7 @@ module OS
           checks.freeze
         end
 
+        sig { returns(T::Array[String]) }
         def fatal_build_from_source_checks
           %w[
             check_xcode_license_approved
@@ -69,6 +80,7 @@ module OS
           ].freeze
         end
 
+        sig { returns(T::Array[String]) }
         def fatal_setup_build_environment_checks
           %w[
             check_xcode_minimum_version
@@ -77,12 +89,14 @@ module OS
           ].freeze
         end
 
+        sig { returns(T::Array[String]) }
         def supported_configuration_checks
           %w[
             check_for_unsupported_macos
           ].freeze
         end
 
+        sig { returns(T::Array[String]) }
         def build_from_source_checks
           %w[
             check_for_installed_developer_tools
@@ -91,6 +105,7 @@ module OS
           ].freeze
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_non_prefixed_findutils
           findutils = ::Formula["findutils"]
           return unless findutils.any_version_installed?
@@ -106,6 +121,7 @@ module OS
           nil
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_unsupported_macos
           return if Homebrew::EnvConfig.developer?
           return if ENV["HOMEBREW_INTEGRATION_TEST"]
@@ -131,6 +147,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_opencore
           return if ::Hardware::CPU.physical_cpu_arm64?
 
@@ -155,6 +172,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_xcode_up_to_date
           return unless MacOS::Xcode.outdated?
 
@@ -191,6 +209,7 @@ module OS
           message
         end
 
+        sig { returns(T.nilable(String)) }
         def check_clt_up_to_date
           return unless MacOS::CLT.outdated?
 
@@ -211,6 +230,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_xcode_minimum_version
           return unless MacOS::Xcode.below_minimum_version?
 
@@ -224,6 +244,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_clt_minimum_version
           return unless MacOS::CLT.below_minimum_version?
 
@@ -233,6 +254,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_if_xcode_needs_clt_installed
           return unless MacOS::Xcode.needs_clt_installed?
 
@@ -242,6 +264,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_xcode_prefix
           prefix = MacOS::Xcode.prefix
           return if prefix.nil?
@@ -253,6 +276,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_xcode_prefix_exists
           prefix = MacOS::Xcode.prefix
           return if prefix.nil? || prefix.exist?
@@ -264,6 +288,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_xcode_select_path
           return if MacOS::CLT.installed?
           return unless MacOS::Xcode.installed?
@@ -278,6 +303,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_xcode_license_approved
           # If the user installs Xcode-only, they have to approve the
           # license or no "xc*" tool will work.
@@ -291,6 +317,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_filesystem_case_sensitive
           dirs_to_check = [
             HOMEBREW_PREFIX,
@@ -324,6 +351,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_gettext
           find_relative_paths("lib/libgettextlib.dylib",
                               "lib/libintl.dylib",
@@ -359,6 +387,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_iconv
           find_relative_paths("lib/libiconv.dylib", "include/iconv.h")
           return if @found.empty?
@@ -389,6 +418,7 @@ module OS
           end
         end
 
+        sig { returns(T.nilable(String)) }
         def check_for_multiple_volumes
           return unless HOMEBREW_CELLAR.exist?
 
@@ -424,6 +454,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_if_supported_sdk_available
           return unless ::DevelopmentTools.installed?
           return unless MacOS.sdk_root_needed?
@@ -454,6 +485,7 @@ module OS
         # The CLT 10.x -> 11.x upgrade process on 10.14 contained a bug which broke the SDKs.
         # Notably, MacOSX10.14.sdk would indirectly symlink to MacOSX10.15.sdk.
         # This diagnostic was introduced to check for this and recommend a full reinstall.
+        sig { returns(T.nilable(String)) }
         def check_broken_sdks
           locator = MacOS.sdk_locator
 
@@ -485,6 +517,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_cask_software_versions
           super
           add_info "macOS", MacOS.full_version
@@ -507,6 +540,7 @@ module OS
           nil
         end
 
+        sig { returns(T.nilable(String)) }
         def check_pkgconf_macos_sdk_mismatch
           # We don't provide suitable bottles for these versions.
           return if OS::Mac.version.prerelease? || OS::Mac.version.outdated_release?
@@ -543,6 +577,7 @@ module OS
           EOS
         end
 
+        sig { returns(T.nilable(String)) }
         def check_cask_quarantine_support
           status, check_output = ::Cask::Quarantine.check_quarantine_support