diff --git a/Library/Homebrew/cask/url.rb b/Library/Homebrew/cask/url.rb
index 71489fcdde..f11ee49747 100644
--- a/Library/Homebrew/cask/url.rb
+++ b/Library/Homebrew/cask/url.rb
@@ -54,7 +54,7 @@ module Cask
         revisions:       T.nilable(T::Hash[T.any(Symbol, String), String]),
         revision:        T.nilable(String),
         trust_cert:      T.nilable(T::Boolean),
-        cookies:         T.nilable(T::Hash[String, String]),
+        cookies:         T.nilable(T::Hash[T.any(String, Symbol), String]),
         referer:         T.nilable(T.any(URI::Generic, String)),
         header:          T.nilable(T.any(String, T::Array[String])),
         user_agent:      T.nilable(T.any(Symbol, String)),
@@ -80,7 +80,7 @@ module Cask
       specs[:revisions]  = @revisions  = T.let(revisions, T.nilable(T::Hash[T.any(Symbol, String), String]))
       specs[:revision]   = @revision   = T.let(revision, T.nilable(String))
       specs[:trust_cert] = @trust_cert = T.let(trust_cert, T.nilable(T::Boolean))
-      specs[:cookies]    = @cookies    = T.let(cookies, T.nilable(T::Hash[String, String]))
+      specs[:cookies]    = @cookies    = T.let(cookies, T.nilable(T::Hash[T.any(String, Symbol), String]))
       specs[:referer]    = @referer    = T.let(referer, T.nilable(T.any(URI::Generic, String)))
       specs[:headers]    = @header     = T.let(header, T.nilable(T.any(String, T::Array[String])))
       specs[:user_agent] = @user_agent = T.let(user_agent || :default, T.nilable(T.any(Symbol, String)))
diff --git a/Library/Homebrew/cmd/outdated.rb b/Library/Homebrew/cmd/outdated.rb
index 6b4d81f179..3b9761c2dd 100644
--- a/Library/Homebrew/cmd/outdated.rb
+++ b/Library/Homebrew/cmd/outdated.rb
@@ -127,9 +127,7 @@ module Homebrew
       sig {
         params(
           formulae_or_casks: T::Array[T.any(Formula, Cask::Cask)],
-        ).returns(
-          T::Array[T.any(T::Hash[String, T.untyped], T::Hash[String, T.untyped])],
-        )
+        ).returns(T::Array[T::Hash[Symbol, T.untyped]])
       }
       def json_info(formulae_or_casks)
         formulae_or_casks.map do |formula_or_cask|
diff --git a/Library/Homebrew/diagnostic.rb b/Library/Homebrew/diagnostic.rb
index b00517b557..9dbcb63ce9 100644
--- a/Library/Homebrew/diagnostic.rb
+++ b/Library/Homebrew/diagnostic.rb
@@ -1198,9 +1198,9 @@ module Homebrew
 
       private
 
-      sig { returns(T::Array[Pathname]) }
+      sig { returns(T::Array[String]) }
       def paths
-        @paths ||= T.let(ORIGINAL_PATHS.uniq.map(&:to_s), T.nilable(T::Array[Pathname]))
+        @paths ||= T.let(ORIGINAL_PATHS.uniq.map(&:to_s), T.nilable(T::Array[String]))
       end
     end
   end
diff --git a/Library/Homebrew/test/formula_spec.rb b/Library/Homebrew/test/formula_spec.rb
index 6eefa7b2dc..b3225648b9 100644
--- a/Library/Homebrew/test/formula_spec.rb
+++ b/Library/Homebrew/test/formula_spec.rb
@@ -185,7 +185,7 @@ RSpec.describe Formula do
 
     build_values_with_no_installed_alias = [
       BuildOptions.new(Options.new, f.options),
-      Tab.new(source: { "path" => f.path.to_s }),
+      Tab.new("source" => { "path" => f.path.to_s }),
     ]
     build_values_with_no_installed_alias.each do |build|
       f.build = build
@@ -201,7 +201,7 @@ RSpec.describe Formula do
     CoreTap.instance.alias_dir.mkpath
     FileUtils.ln_sf f.path, alias_path
 
-    f.build = Tab.new(source: { "path" => alias_path.to_s })
+    f.build = Tab.new("source" => { "path" => alias_path.to_s })
 
     expect(f.installed_alias_path).to eq(alias_path)
     expect(f.installed_alias_name).to eq(alias_name)
@@ -220,7 +220,7 @@ RSpec.describe Formula do
 
     build_values_with_no_installed_alias = [
       BuildOptions.new(Options.new, f.options),
-      Tab.new(source: { "path" => f.path.to_s }),
+      Tab.new("source" => { "path" => f.path.to_s }),
     ]
     build_values_with_no_installed_alias.each do |build|
       f.build = build
@@ -237,7 +237,7 @@ RSpec.describe Formula do
     tap.alias_dir.mkpath
     FileUtils.ln_sf f.path, alias_path
 
-    f.build = Tab.new(source: { "path" => alias_path.to_s })
+    f.build = Tab.new("source" => { "path" => alias_path.to_s })
 
     expect(f.installed_alias_path).to eq(alias_path)
     expect(f.installed_alias_name).to eq(alias_name)
@@ -440,7 +440,7 @@ RSpec.describe Formula do
       f = formula(alias_path:) do
         url "foo-1.0"
       end
-      f.build = Tab.new(source: { "path" => source_path.to_s })
+      f.build = Tab.new("source" => { "path" => source_path.to_s })
 
       expect(f.alias_path).to eq(alias_path)
       expect(f.installed_alias_path).to be_nil
@@ -453,7 +453,7 @@ RSpec.describe Formula do
       f = formula(alias_path:) do
         url "foo-1.0"
       end
-      f.build = Tab.new(source: { "path" => source_path.to_s })
+      f.build = Tab.new("source" => { "path" => source_path.to_s })
       CoreTap.instance.alias_dir.mkpath
       FileUtils.ln_sf f.path, source_path