diff --git a/Library/Homebrew/cask/audit.rb b/Library/Homebrew/cask/audit.rb
index 56f7f1e3de..70412cce30 100644
--- a/Library/Homebrew/cask/audit.rb
+++ b/Library/Homebrew/cask/audit.rb
@@ -381,12 +381,15 @@ module Cask
     sig { void }
     def audit_token_conflicts
       return unless token_conflicts?
-      return unless core_formula_names.include?(cask.token)
 
-      add_error(
-        "possible duplicate, cask token conflicts with Homebrew core formula: #{Formatter.url(core_formula_url)}",
-        strict_only: true,
-      )
+      Homebrew.with_no_api_env do
+        return unless core_formula_names.include?(cask.token)
+
+        add_error(
+          "possible duplicate, cask token conflicts with Homebrew core formula: #{Formatter.url(core_formula_url)}",
+          strict_only: true,
+        )
+      end
     end
 
     sig { void }
@@ -846,7 +849,10 @@ module Cask
 
     sig { returns(String) }
     def core_formula_url
-      "#{core_tap.default_remote}/blob/HEAD/Formula/#{cask.token}.rb"
+      formula_path = Formulary.core_path(cask.token)
+                              .to_s
+                              .delete_prefix(core_tap.path.to_s)
+      "#{core_tap.default_remote}/blob/HEAD/Formula/#{formula_path}"
     end
   end
 end
diff --git a/Library/Homebrew/cask/cask_loader.rb b/Library/Homebrew/cask/cask_loader.rb
index bcf12b04d2..c343f491db 100644
--- a/Library/Homebrew/cask/cask_loader.rb
+++ b/Library/Homebrew/cask/cask_loader.rb
@@ -439,7 +439,7 @@ module Cask
     end
 
     def self.default_path(token)
-      CoreCaskTap.instance.cask_dir/"#{token.to_s.downcase}.rb"
+      find_cask_in_tap(token.to_s.downcase, CoreCaskTap.instance)
     end
 
     def self.tap_paths(token, warn: true)
@@ -455,7 +455,8 @@ module Cask
     def self.find_cask_in_tap(token, tap)
       filename = "#{token}.rb"
 
-      Tap.cask_files_by_name(tap).fetch(filename, tap.cask_dir/filename)
+      Tap.cask_files_by_name(tap)
+         .fetch(token, tap.cask_dir/filename)
     end
   end
 end
diff --git a/Library/Homebrew/cli/named_args.rb b/Library/Homebrew/cli/named_args.rb
index 37ffa4bbcb..98ab981c18 100644
--- a/Library/Homebrew/cli/named_args.rb
+++ b/Library/Homebrew/cli/named_args.rb
@@ -227,40 +227,42 @@ module Homebrew
       sig { params(only: T.nilable(Symbol), recurse_tap: T::Boolean).returns(T::Array[Pathname]) }
       def to_paths(only: parent&.only_formula_or_cask, recurse_tap: false)
         @to_paths ||= {}
-        @to_paths[only] ||= downcased_unique_named.flat_map do |name|
-          path = Pathname(name)
-          if File.exist?(name)
-            path
-          elsif name.count("/") == 1 && !name.start_with?("./", "/")
-            tap = Tap.fetch(name)
+        @to_paths[only] ||= Homebrew.with_no_api_env_if_needed(@without_api) do
+          downcased_unique_named.flat_map do |name|
+            path = Pathname(name)
+            if File.exist?(name)
+              path
+            elsif name.count("/") == 1 && !name.start_with?("./", "/")
+              tap = Tap.fetch(name)
 
-            if recurse_tap
-              next tap.formula_files if only == :formula
-              next tap.cask_files if only == :cask
+              if recurse_tap
+                next tap.formula_files if only == :formula
+                next tap.cask_files if only == :cask
+              end
+
+              tap.path
+            else
+              next Formulary.path(name) if only == :formula
+              next Cask::CaskLoader.path(name) if only == :cask
+
+              formula_path = Formulary.path(name)
+              cask_path = Cask::CaskLoader.path(name)
+
+              paths = []
+
+              if formula_path.exist? ||
+                 (!CoreTap.instance.installed? && Homebrew::API::Formula.all_formulae.key?(path.basename))
+                paths << formula_path
+              end
+              if cask_path.exist? ||
+                 (!CoreCaskTap.instance.installed? && Homebrew::API::Cask.all_casks.key?(path.basename))
+                paths << cask_path
+              end
+
+              paths.empty? ? path : paths
             end
-
-            tap.path
-          else
-            next Formulary.path(name) if only == :formula
-            next Cask::CaskLoader.path(name) if only == :cask
-
-            formula_path = Formulary.path(name)
-            cask_path = Cask::CaskLoader.path(name)
-
-            paths = []
-
-            if formula_path.exist? ||
-               (!CoreTap.instance.installed? && Homebrew::API::Formula.all_formulae.key?(path.basename))
-              paths << formula_path
-            end
-            if cask_path.exist? ||
-               (!CoreCaskTap.instance.installed? && Homebrew::API::Cask.all_casks.key?(path.basename))
-              paths << cask_path
-            end
-
-            paths.empty? ? path : paths
-          end
-        end.uniq.freeze
+          end.uniq.freeze
+        end
       end
 
       sig { returns(T::Array[Keg]) }
diff --git a/Library/Homebrew/cmd/log.rb b/Library/Homebrew/cmd/log.rb
index a0f56165b4..35a6033de6 100644
--- a/Library/Homebrew/cmd/log.rb
+++ b/Library/Homebrew/cmd/log.rb
@@ -29,7 +29,7 @@ module Homebrew
       conflicts "-1", "--max-count"
       conflicts "--formula", "--cask"
 
-      named_args [:formula, :cask], max: 1
+      named_args [:formula, :cask], max: 1, without_api: true
     end
   end
 
diff --git a/Library/Homebrew/dev-cmd/create.rb b/Library/Homebrew/dev-cmd/create.rb
index e0e3c5d5e1..f02b61769a 100644
--- a/Library/Homebrew/dev-cmd/create.rb
+++ b/Library/Homebrew/dev-cmd/create.rb
@@ -96,7 +96,7 @@ module Homebrew
     cask_tap = Tap.fetch(args.tap || "homebrew/cask")
     raise TapUnavailableError, cask_tap.name unless cask_tap.installed?
 
-    cask_path = Cask::CaskLoader.path("#{cask_tap}/#{token}")
+    cask_path = cask_tap.new_cask_path(token)
     cask_path.dirname.mkpath unless cask_path.dirname.exist?
     raise Cask::CaskAlreadyCreatedError, token if cask_path.exist?
 
diff --git a/Library/Homebrew/dev-cmd/extract.rb b/Library/Homebrew/dev-cmd/extract.rb
index 58ab33a0b2..9b17567d75 100644
--- a/Library/Homebrew/dev-cmd/extract.rb
+++ b/Library/Homebrew/dev-cmd/extract.rb
@@ -114,7 +114,7 @@ module Homebrew
 
     repo = source_tap.path
     pattern = if source_tap.core_tap?
-      [repo/"Formula/#{name}.rb"]
+      [source_tap.new_formula_path(name), repo/"Formula/#{name}.rb"].uniq
     else
       # A formula can technically live in the root directory of a tap or in any of its subdirectories
       [repo/"#{name}.rb", repo/"**/#{name}.rb"]
diff --git a/Library/Homebrew/dev-cmd/pr-pull.rb b/Library/Homebrew/dev-cmd/pr-pull.rb
index 479167bdc4..82a60194c7 100644
--- a/Library/Homebrew/dev-cmd/pr-pull.rb
+++ b/Library/Homebrew/dev-cmd/pr-pull.rb
@@ -110,7 +110,7 @@ module Homebrew
   end
 
   def self.get_package(tap, subject_name, subject_path, content)
-    if subject_path.dirname == tap.cask_dir
+    if subject_path.to_s.start_with?("#{tap.cask_dir}/")
       cask = begin
         Cask::CaskLoader.load(content.dup)
       rescue Cask::CaskUnavailableError
@@ -130,7 +130,7 @@ module Homebrew
     subject_path = Pathname(subject_path)
     tap          = Tap.from_path(subject_path)
     subject_name = subject_path.basename.to_s.chomp(".rb")
-    is_cask      = subject_path.dirname == tap.cask_dir
+    is_cask      = subject_path.to_s.start_with?("#{tap.cask_dir}/")
     name         = is_cask ? "cask" : "formula"
 
     new_package = get_package(tap, subject_name, subject_path, new_contents)
@@ -241,8 +241,8 @@ module Homebrew
       files.each do |file|
         files_to_commits[file] ||= []
         files_to_commits[file] << commit
-        tap_file = tap.path/file
-        if (tap_file.dirname == tap.formula_dir || tap_file.dirname == tap.cask_dir) &&
+        tap_file = (tap.path/file).to_s
+        if (tap_file.start_with?("#{tap.formula_dir}/") || tap_file.start_with?("#{tap.cask_dir}/")) &&
            File.extname(file) == ".rb"
           next
         end
diff --git a/Library/Homebrew/formula_creator.rb b/Library/Homebrew/formula_creator.rb
index dd4a3701ef..d5e8dc92c6 100644
--- a/Library/Homebrew/formula_creator.rb
+++ b/Library/Homebrew/formula_creator.rb
@@ -45,7 +45,7 @@ module Homebrew
     def update_path
       return if @name.nil? || @tap.nil?
 
-      @path = Formulary.path "#{@tap}/#{@name}"
+      @path = @tap.new_formula_path(@name)
     end
 
     def fetch?
diff --git a/Library/Homebrew/formula_path.sh b/Library/Homebrew/formula_path.sh
index bab691b2c7..c23174971c 100644
--- a/Library/Homebrew/formula_path.sh
+++ b/Library/Homebrew/formula_path.sh
@@ -49,7 +49,7 @@ homebrew-formula-path() {
     local formula_path
     formula_path="$(
       shopt -s nullglob
-      echo "${HOMEBREW_REPOSITORY}/Library/Taps"/*/*/{Formula/,HomebrewFormula/,}"${formula}.rb"
+      echo "${HOMEBREW_REPOSITORY}/Library/Taps"/*/*/{Formula/,HomebrewFormula/,Formula/*/,}"${formula}.rb"
     )"
     [[ -n "${formula_path}" ]] && formula_exists="1"
   fi
diff --git a/Library/Homebrew/formulary.rb b/Library/Homebrew/formulary.rb
index cd014e72f3..0123a79b3e 100644
--- a/Library/Homebrew/formulary.rb
+++ b/Library/Homebrew/formulary.rb
@@ -1003,10 +1003,15 @@ module Formulary
     end.select(&:file?)
   end
 
+  sig { params(name: String, tap: Tap).returns(Pathname) }
   def self.find_formula_in_tap(name, tap)
-    filename = name.dup
-    filename << ".rb" unless filename.end_with?(".rb")
+    filename = if name.end_with?(".rb")
+      name
+    else
+      "#{name}.rb"
+    end
 
-    Tap.formula_files_by_name(tap).fetch(filename, tap.formula_dir/filename)
+    Tap.formula_files_by_name(tap)
+       .fetch(name, tap.formula_dir/filename)
   end
 end
diff --git a/Library/Homebrew/readall.rb b/Library/Homebrew/readall.rb
index 09f5f75861..a165a4351f 100644
--- a/Library/Homebrew/readall.rb
+++ b/Library/Homebrew/readall.rb
@@ -31,7 +31,7 @@ module Readall
           failed = true
         end
 
-        if (formula_dir/"#{f.basename}.rb").exist?
+        if formula_dir.glob("**/#{f.basename}.rb").any?(&:exist?)
           onoe "Formula duplicating alias: #{f}"
           failed = true
         end
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 73a71a29e8..0af9421b5c 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -500,12 +500,22 @@ class Tap
     @potential_formula_dirs ||= [path/"Formula", path/"HomebrewFormula", path].freeze
   end
 
+  sig { params(name: String).returns(Pathname) }
+  def new_formula_path(name)
+    formula_dir/"#{name.downcase}.rb"
+  end
+
   # Path to the directory of all {Cask} files for this {Tap}.
   sig { returns(Pathname) }
   def cask_dir
     @cask_dir ||= path/"Casks"
   end
 
+  sig { params(token: String).returns(Pathname) }
+  def new_cask_path(token)
+    cask_dir/"#{token.downcase}.rb"
+  end
+
   def contents
     contents = []
 
@@ -555,7 +565,7 @@ class Tap
     formula_files.each_with_object({}) do |file, hash|
       # If there's more than one file with the same basename: intentionally
       # ignore the later ones here.
-      hash[file.basename.to_s] ||= file
+      hash[file.basename(".rb").to_s] ||= file
     end
   end
 
@@ -584,7 +594,7 @@ class Tap
     cask_files.each_with_object({}) do |file, hash|
       # If there's more than one file with the same basename: intentionally
       # ignore the later ones here.
-      hash[file.basename.to_s] ||= file
+      hash[file.basename(".rb").to_s] ||= file
     end
   end
 
@@ -984,6 +994,19 @@ class CoreTap < AbstractCoreTap
     end
   end
 
+  sig { params(name: String).returns(Pathname) }
+  def new_formula_path(name)
+    formula_subdir = if name.start_with?("lib")
+      "lib"
+    else
+      name[0].to_s
+    end
+
+    return super unless (formula_dir/formula_subdir).directory?
+
+    formula_dir/formula_subdir/"#{name.downcase}.rb"
+  end
+
   # @private
   sig { returns(Pathname) }
   def alias_dir
@@ -1108,6 +1131,15 @@ class CoreCaskTap < AbstractCoreTap
     true
   end
 
+  sig { params(token: String).returns(Pathname) }
+  def new_cask_path(token)
+    cask_subdir = token[0].to_s
+
+    return super unless (cask_dir/cask_subdir).directory?
+
+    cask_dir/cask_subdir/"#{token.downcase}.rb"
+  end
+
   sig { override.returns(T::Array[Pathname]) }
   def cask_files
     return super if Homebrew::EnvConfig.no_install_from_api? || installed?
diff --git a/Library/Homebrew/test/cleanup_spec.rb b/Library/Homebrew/test/cleanup_spec.rb
index 345a6c5c99..00054edaf0 100644
--- a/Library/Homebrew/test/cleanup_spec.rb
+++ b/Library/Homebrew/test/cleanup_spec.rb
@@ -333,7 +333,7 @@ describe Homebrew::Cleanup do
         FileUtils.touch testball
         FileUtils.touch testball_resource
         (HOMEBREW_CELLAR/"testball"/"0.0.1").mkpath
-        FileUtils.touch(CoreTap.instance.formula_dir/"testball.rb")
+        FileUtils.touch(CoreTap.instance.new_formula_path("testball"))
       end
 
       it "cleans up file if outdated" do
diff --git a/Library/Homebrew/test/dev-cmd/create_spec.rb b/Library/Homebrew/test/dev-cmd/create_spec.rb
index 68589217f9..e0026dd19f 100644
--- a/Library/Homebrew/test/dev-cmd/create_spec.rb
+++ b/Library/Homebrew/test/dev-cmd/create_spec.rb
@@ -4,7 +4,7 @@ require "cmd/shared_examples/args_parse"
 
 describe "brew create" do
   let(:url) { "file://#{TEST_FIXTURE_DIR}/tarballs/testball-0.1.tbz" }
-  let(:formula_file) { CoreTap.new.formula_dir/"testball.rb" }
+  let(:formula_file) { CoreTap.new.new_formula_path("testball") }
 
   it_behaves_like "parseable arguments"
 
diff --git a/Library/Homebrew/test/formula_installer_spec.rb b/Library/Homebrew/test/formula_installer_spec.rb
index 49404f8208..b9c8ae33a1 100644
--- a/Library/Homebrew/test/formula_installer_spec.rb
+++ b/Library/Homebrew/test/formula_installer_spec.rb
@@ -82,7 +82,7 @@ describe FormulaInstaller do
       ENV["HOMEBREW_DEVELOPER"] = "1"
 
       dep_name = "homebrew-test-cyclic"
-      dep_path = CoreTap.new.formula_dir/"#{dep_name}.rb"
+      dep_path = CoreTap.new.new_formula_path(dep_name)
       dep_path.write <<~RUBY
         class #{Formulary.class_s(dep_name)} < Formula
           url "foo"
@@ -105,7 +105,7 @@ describe FormulaInstaller do
 
       formula1_name = "homebrew-test-formula1"
       formula2_name = "homebrew-test-formula2"
-      formula1_path = CoreTap.new.formula_dir/"#{formula1_name}.rb"
+      formula1_path = CoreTap.new.new_formula_path(formula1_name)
       formula1_path.write <<~RUBY
         class #{Formulary.class_s(formula1_name)} < Formula
           url "foo"
@@ -116,7 +116,7 @@ describe FormulaInstaller do
       Formulary.cache.delete(formula1_path)
       formula1 = Formulary.factory(formula1_name)
 
-      formula2_path = CoreTap.new.formula_dir/"#{formula2_name}.rb"
+      formula2_path = CoreTap.new.new_formula_path(formula2_name)
       formula2_path.write <<~RUBY
         class #{Formulary.class_s(formula2_name)} < Formula
           url "foo"
@@ -135,7 +135,7 @@ describe FormulaInstaller do
 
     it "raises on pinned dependency" do
       dep_name = "homebrew-test-dependency"
-      dep_path = CoreTap.new.formula_dir/"#{dep_name}.rb"
+      dep_path = CoreTap.new.new_formula_path(dep_name)
       dep_path.write <<~RUBY
         class #{Formulary.class_s(dep_name)} < Formula
           url "foo"
diff --git a/Library/Homebrew/test/formula_spec.rb b/Library/Homebrew/test/formula_spec.rb
index c8e3fb4c78..5f4a6765d4 100644
--- a/Library/Homebrew/test/formula_spec.rb
+++ b/Library/Homebrew/test/formula_spec.rb
@@ -429,7 +429,7 @@ describe Formula do
 
     example "alias paths with tab with non alias source path" do
       alias_path = (CoreTap.instance.alias_dir/"another_name")
-      source_path = (CoreTap.instance.formula_dir/"another_other_name")
+      source_path = CoreTap.instance.new_formula_path("another_other_name")
 
       f = formula alias_path: alias_path do
         url "foo-1.0"
@@ -940,7 +940,7 @@ describe Formula do
   end
 
   describe "#to_hash_with_variations", :needs_macos do
-    let(:formula_path) { CoreTap.new.formula_dir/"foo-variations.rb" }
+    let(:formula_path) { CoreTap.new.new_formula_path("foo-variations") }
     let(:formula_content) do
       <<~RUBY
         class FooVariations < Formula
diff --git a/Library/Homebrew/test/formulary_spec.rb b/Library/Homebrew/test/formulary_spec.rb
index ad81b0aa83..7c237cc4b4 100644
--- a/Library/Homebrew/test/formulary_spec.rb
+++ b/Library/Homebrew/test/formulary_spec.rb
@@ -6,7 +6,7 @@ require "utils/bottles"
 
 describe Formulary do
   let(:formula_name) { "testball_bottle" }
-  let(:formula_path) { CoreTap.new.formula_dir/"#{formula_name}.rb" }
+  let(:formula_path) { CoreTap.new.new_formula_path(formula_name) }
   let(:formula_content) do
     <<~RUBY
       class #{described_class.class_s(formula_name)} < Formula
@@ -84,7 +84,11 @@ describe Formulary do
       before { CoreTap.instance.clear_cache }
 
       let(:formula_name) { "testball_sharded" }
-      let(:formula_path) { CoreTap.new.formula_dir/formula_name[0]/"#{formula_name}.rb" }
+      let(:formula_path) do
+        core_tap = CoreTap.new
+        (core_tap.formula_dir/formula_name[0]).mkpath
+        core_tap.new_formula_path(formula_name)
+      end
 
       it "returns a Formula" do
         expect(described_class.factory(formula_name)).to be_a(Formula)
diff --git a/Library/Homebrew/test/support/helper/spec/shared_examples/formulae_exist.rb b/Library/Homebrew/test/support/helper/spec/shared_examples/formulae_exist.rb
index b005657977..9dcbf60b31 100644
--- a/Library/Homebrew/test/support/helper/spec/shared_examples/formulae_exist.rb
+++ b/Library/Homebrew/test/support/helper/spec/shared_examples/formulae_exist.rb
@@ -4,9 +4,9 @@ shared_examples "formulae exist" do |array|
   array.each do |f|
     it "#{f} formula exists" do
       core_tap = Pathname("#{HOMEBREW_LIBRARY_PATH}/../Taps/homebrew/homebrew-core")
-      formula_path = core_tap/"Formula/#{f}.rb"
+      formula_paths = core_tap.glob("Formula/**/#{f}.rb")
       alias_path = core_tap/"Aliases/#{f}"
-      expect(formula_path.exist? || alias_path.exist?).to be true
+      expect(formula_paths.any?(&:exist?) || alias_path.exist?).to be true
     end
   end
 end