diff --git a/Library/Homebrew/cask/tab.rb b/Library/Homebrew/cask/tab.rb
index b6bc7a54da..6ba4b027d7 100644
--- a/Library/Homebrew/cask/tab.rb
+++ b/Library/Homebrew/cask/tab.rb
@@ -11,7 +11,7 @@ module Cask
     sig { returns(T.nilable(T::Array[T.untyped])) }
     attr_accessor :uninstall_artifacts
 
-    sig { params(attributes: T::Hash[String, T.untyped]).void }
+    sig { params(attributes: T::Hash[T.any(String, Symbol), T.untyped]).void }
     def initialize(attributes = {})
       @uninstall_flight_blocks = T.let(nil, T.nilable(T::Boolean))
       @uninstall_artifacts = T.let(nil, T.nilable(T::Array[T.untyped]))
diff --git a/Library/Homebrew/cask/url.rb b/Library/Homebrew/cask/url.rb
index f11ee49747..c87a7b2198 100644
--- a/Library/Homebrew/cask/url.rb
+++ b/Library/Homebrew/cask/url.rb
@@ -80,7 +80,8 @@ 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[T.any(String, Symbol), String]))
+      specs[:cookies]    =
+        @cookies = T.let(cookies&.transform_keys(&:to_s), T.nilable(T::Hash[String, 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/system_command.rb b/Library/Homebrew/system_command.rb
index 1ba0ff80e9..bf2b823566 100644
--- a/Library/Homebrew/system_command.rb
+++ b/Library/Homebrew/system_command.rb
@@ -169,7 +169,7 @@ class SystemCommand
       args:         T::Array[T.any(String, Integer, Float, Pathname, URI::Generic)],
       sudo:         T::Boolean,
       sudo_as_root: T::Boolean,
-      env:          T::Hash[String, String],
+      env:          T::Hash[String, T.nilable(String)],
       input:        T.any(String, T::Array[String]),
       must_succeed: T::Boolean,
       print_stdout: T.any(T::Boolean, Symbol),
diff --git a/Library/Homebrew/tab.rb b/Library/Homebrew/tab.rb
index 9acea83252..799d4c2c94 100644
--- a/Library/Homebrew/tab.rb
+++ b/Library/Homebrew/tab.rb
@@ -38,7 +38,7 @@ class AbstractTab
   # @api internal
   attr_accessor :runtime_dependencies
 
-  sig { params(attributes: T::Hash[String, T.untyped]).void }
+  sig { params(attributes: T::Hash[T.any(String, Symbol), T.untyped]).void }
   def initialize(attributes = {})
     @installed_as_dependency = T.let(nil, T.nilable(T::Boolean))
     @installed_on_request = T.let(nil, T.nilable(T::Boolean))
@@ -170,7 +170,7 @@ class Tab < AbstractTab
   attr_writer :used_options, :unused_options, :compiler, :source_modified_time
   attr_reader :tapped_from
 
-  sig { params(attributes: T::Hash[String, T.untyped]).void }
+  sig { params(attributes: T::Hash[T.any(String, Symbol), T.untyped]).void }
   def initialize(attributes = {})
     @poured_from_bottle = T.let(nil, T.nilable(T::Boolean))
     @built_as_bottle = T.let(nil, T.nilable(T::Boolean))
diff --git a/Library/Homebrew/test/formula_spec.rb b/Library/Homebrew/test/formula_spec.rb
index b3225648b9..9925d05ce6 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
 
@@ -919,7 +919,7 @@ RSpec.describe Formula do
     f1 = formula "f1" do
       url "f1-1"
 
-      depends_on xcode: ["1.0", "optional"]
+      depends_on xcode: ["1.0", :optional]
     end
     stub_formula_loader(f1)
 
diff --git a/Library/Homebrew/test/tab_spec.rb b/Library/Homebrew/test/tab_spec.rb
index bb76ce77d2..594e9c7747 100644
--- a/Library/Homebrew/test/tab_spec.rb
+++ b/Library/Homebrew/test/tab_spec.rb
@@ -116,7 +116,7 @@ RSpec.describe Tab do
     tab = described_class.new
     expect(tab.parsed_homebrew_version).to be Version::NULL
 
-    tab = described_class.new("homebrew_version" => "1.2.3")
+    tab = described_class.new(homebrew_version: "1.2.3")
     expect(tab.parsed_homebrew_version).to eq("1.2.3")
     expect(tab.parsed_homebrew_version).to be < "1.2.3-1-g12789abdf"
     expect(tab.parsed_homebrew_version).to be_a(Version)
@@ -126,7 +126,7 @@ RSpec.describe Tab do
     expect(tab.parsed_homebrew_version).to be > "1.2.4-566-g21789abdf"
     expect(tab.parsed_homebrew_version).to be < "1.2.4-568-g01789abdf"
 
-    tab = described_class.new("homebrew_version" => "2.0.0-134-gabcdefabc-dirty")
+    tab = described_class.new(homebrew_version: "2.0.0-134-gabcdefabc-dirty")
     expect(tab.parsed_homebrew_version).to be > "2.0.0"
     expect(tab.parsed_homebrew_version).to be > "2.0.0-133-g21789abdf"
     expect(tab.parsed_homebrew_version).to be < "2.0.0-135-g01789abdf"
@@ -486,10 +486,10 @@ RSpec.describe Tab do
 
     it "returns install information for the Tab" do
       tab = described_class.new(
-        "poured_from_bottle" => true,
-        "loaded_from_api"    => true,
-        "time"               => 1_720_189_863,
-        "used_options"       => %w[--with-foo --without-bar],
+        poured_from_bottle: true,
+        loaded_from_api:    true,
+        time:               1_720_189_863,
+        used_options:       %w[--with-foo --without-bar],
       )
       output = "Poured from bottle using the formulae.brew.sh API on #{time_string} " \
                "with: --with-foo --without-bar"
@@ -497,42 +497,42 @@ RSpec.describe Tab do
     end
 
     it "includes 'Poured from bottle' if the formula was installed from a bottle" do
-      tab = described_class.new("poured_from_bottle" =>  true)
+      tab = described_class.new(poured_from_bottle: true)
       expect(tab.to_s).to include("Poured from bottle")
     end
 
     it "includes 'Built from source' if the formula was not installed from a bottle" do
-      tab = described_class.new("poured_from_bottle" => false)
+      tab = described_class.new(poured_from_bottle: false)
       expect(tab.to_s).to include("Built from source")
     end
 
     it "includes 'using the formulae.brew.sh API' if the formula was installed from the API" do
-      tab = described_class.new("loaded_from_api" => true)
+      tab = described_class.new(loaded_from_api: true)
       expect(tab.to_s).to include("using the formulae.brew.sh API")
     end
 
     it "does not include 'using the formulae.brew.sh API' if the formula was not installed from the API" do
-      tab = described_class.new("loaded_from_api" => false)
+      tab = described_class.new(loaded_from_api: false)
       expect(tab.to_s).not_to include("using the formulae.brew.sh API")
     end
 
     it "includes the time value if specified" do
-      tab = described_class.new("time" => 1_720_189_863)
+      tab = described_class.new(time: 1_720_189_863)
       expect(tab.to_s).to include("on #{time_string}")
     end
 
     it "does not include the time value if not specified" do
-      tab = described_class.new("time" =>  nil)
+      tab = described_class.new(time: nil)
       expect(tab.to_s).not_to match(/on %d+-%d+-%d+ at %d+:%d+:%d+/)
     end
 
     it "includes options if specified" do
-      tab = described_class.new("used_options" => %w[--with-foo --without-bar])
+      tab = described_class.new(used_options: %w[--with-foo --without-bar])
       expect(tab.to_s).to include("with: --with-foo --without-bar")
     end
 
     it "not to include options if not specified" do
-      tab = described_class.new("used_options" => [])
+      tab = described_class.new(used_options: [])
       expect(tab.to_s).not_to include("with: ")
     end
   end