diagnostic: add check for broken taps

Detect half-baked core taps that show up on a fairly regular basis (e.g. #11465).

The logic is simple enough: Since an improper tap wouldn't have a complete Git config, and is always somewhere below `HOMEBREW_REPOSITORY`, any Git operation would look at the Brew repo instead. We simply need to test for any of:

1. Empty tap origin
2. Empty tap HEAD
3. Tap HEAD == Brew HEAD

Library/Homebrew/diagnostic.rb

@@ -147,6 +147,27 @@ def examine_git_origin(repository_path, desired_origin)
         end
       end
 
+      def broken_tap_msg(tap)
+        <<~EOS
+          #{tap.full_name} was not tapped properly.
+          To fix:
+            rm -rf "#{tap.path}"
+            brew tap #{tap.name}
+        EOS
+      end
+
+      def broken_tap(tap)
+        return unless Utils::Git.available?
+        return unless HOMEBREW_REPOSITORY.git?
+
+        return broken_tap_msg(tap) if tap.remote.blank?
+
+        tap_head = tap.git_head
+        return broken_tap_msg(tap) if tap_head.blank?
+
+        return broken_tap_msg(tap) if tap_head == HOMEBREW_REPOSITORY.git_head
+      end
+
       def check_for_installed_developer_tools
         return if DevelopmentTools.installed?
 
@@ -558,15 +579,16 @@ def check_brew_git_origin
         examine_git_origin(HOMEBREW_REPOSITORY, Homebrew::EnvConfig.brew_git_remote)
       end
 
-      def check_coretap_git_origin
-        examine_git_origin(CoreTap.instance.path, Homebrew::EnvConfig.core_git_remote)
+      def check_coretap_integrity
+        coretap = CoreTap.instance
+        broken_tap(coretap) || examine_git_origin(coretap.path, Homebrew::EnvConfig.core_git_remote)
       end
 
-      def check_casktap_git_origin
+      def check_casktap_integrity
         default_cask_tap = Tap.default_cask_tap
         return unless default_cask_tap.installed?
 
-        examine_git_origin(default_cask_tap.path, default_cask_tap.remote)
+        broken_tap(default_cask_tap) || examine_git_origin(default_cask_tap.path, default_cask_tap.remote)
       end
 
       sig { returns(T.nilable(String)) }