diff --git a/Library/Homebrew/formula.rb b/Library/Homebrew/formula.rb
index ff28c685ca61b..3ef26943da25b 100644
--- a/Library/Homebrew/formula.rb
+++ b/Library/Homebrew/formula.rb
@@ -722,8 +722,10 @@ def latest_installed_prefix
   # This directory points to {#opt_prefix} if it exists and if {#prefix} is not
   # called from within the same formula's {#install} or {#post_install} methods.
   # Otherwise, return the full path to the formula's versioned cellar.
+  sig { params(version: T.any(String, PkgVersion)).returns(Pathname) }
   def prefix(version = pkg_version)
     versioned_prefix = versioned_prefix(version)
+    version = PkgVersion.parse(version) if version.is_a?(String)
     if !@prefix_returns_versioned_prefix && version == pkg_version &&
        versioned_prefix.directory? && Keg.new(versioned_prefix).optlinked?
       opt_prefix
diff --git a/Library/Homebrew/pkg_version.rb b/Library/Homebrew/pkg_version.rb
index 6e29244d0e51e..80c693639b764 100644
--- a/Library/Homebrew/pkg_version.rb
+++ b/Library/Homebrew/pkg_version.rb
@@ -1,4 +1,4 @@
-# typed: true # rubocop:todo Sorbet/StrictSigil
+# typed: strict
 # frozen_string_literal: true
 
 require "version"
@@ -11,21 +11,28 @@ class PkgVersion
   REGEX = /\A(.+?)(?:_(\d+))?\z/
   private_constant :REGEX
 
-  attr_reader :version, :revision
+  sig { returns(Version) }
+  attr_reader :version
+
+  sig { returns(Integer) }
+  attr_reader :revision
 
   delegate [:major, :minor, :patch, :major_minor, :major_minor_patch] => :version
 
+  sig { params(path: String).returns(PkgVersion) }
   def self.parse(path)
     _, version, revision = *path.match(REGEX)
-    version = Version.new(version)
+    version = Version.new(version.to_s)
     new(version, revision.to_i)
   end
 
+  sig { params(version: Version, revision: Integer).void }
   def initialize(version, revision)
-    @version = version
-    @revision = revision
+    @version = T.let(version, Version)
+    @revision = T.let(revision, Integer)
   end
 
+  sig { returns(T::Boolean) }
   def head?
     version.head?
   end
@@ -42,9 +49,8 @@ def to_str
   sig { returns(String) }
   def to_s = to_str
 
+  sig { params(other: PkgVersion).returns(T.nilable(Integer)) }
   def <=>(other)
-    return unless other.is_a?(PkgVersion)
-
     version_comparison = (version <=> other.version)
     return if version_comparison.nil?
 
@@ -52,6 +58,7 @@ def <=>(other)
   end
   alias eql? ==
 
+  sig { returns(Integer) }
   def hash
     [version, revision].hash
   end
diff --git a/Library/Homebrew/test/pkg_version_spec.rb b/Library/Homebrew/test/pkg_version_spec.rb
index 578ae2a14f5fc..cbcc2f4393bec 100644
--- a/Library/Homebrew/test/pkg_version_spec.rb
+++ b/Library/Homebrew/test/pkg_version_spec.rb
@@ -33,13 +33,13 @@
     it "raises an error if the other side isn't of the same class" do
       expect do
         described_class.new(Version.new("1.0"), 0) > Object.new
-      end.to raise_error(ArgumentError)
+      end.to raise_error(TypeError)
     end
 
     it "is not compatible with Version" do
       expect do
         described_class.new(Version.new("1.0"), 0) > Version.new("1.0")
-      end.to raise_error(ArgumentError)
+      end.to raise_error(TypeError)
     end
   end
 
@@ -55,12 +55,7 @@
 
   describe "#<=>" do
     it "returns nil if the comparison fails" do
-      expect(described_class.new(Version.new("1.0"), 0) <=> Object.new).to be_nil
       expect(Object.new <=> described_class.new(Version.new("1.0"), 0)).to be_nil
-      expect(Object.new <=> described_class.new(Version.new("1.0"), 0)).to be_nil
-      expect(described_class.new(Version.new("1.0"), 0) <=> nil).to be_nil
-      # This one used to fail due to dereferencing a null `self`
-      expect(described_class.new(nil, 0) <=> described_class.new(Version.new("1.0"), 0)).to be_nil
     end
   end