workflows/build-pkg: actually try to install package.

- This should help avoid this regressing
- Remove existing Homebrew installation(s)
- Install it twice to ensure that installing over the top of an existing
  installation works as expected
- Remove existing API cache to ensure we have the freshest files from
  the API in our package

.github/workflows/build-pkg.yml

@@ -23,6 +23,9 @@ jobs:
       HOMEBREW_NO_ANALYTICS_THIS_RUN: 1
       HOMEBREW_NO_ANALYTICS_MESSAGE_OUTPUT: 1
     steps:
+      - name: Remove existing API cache (to force update)
+        run: rm -rf ~/Library/Caches/Homebrew/api
+
       - name: Set up Homebrew
         id: set-up-homebrew
         uses: Homebrew/actions/setup-homebrew@master
@@ -119,6 +122,15 @@ jobs:
             security delete-keychain "${RUNNER_TEMP}/${TEMPORARY_KEYCHAIN_FILE}"
           fi
 
+      - name: Remove existing Homebrew installations
+        run: sudo rm -rf brew /usr/local/bin/brew /usr/local/.??* /usr/local/Homebrew /usr/local/Caskroom /usr/local/Cellar
+
+      - name: Install Homebrew from installer package
+        run: sudo installer -verbose -pkg Homebrew-${{ steps.print-version.outputs.version }}.pkg -target /
+
+      - name: Install Homebrew (again) from installer package
+        run: sudo installer -verbose -pkg Homebrew-${{ steps.print-version.outputs.version }}.pkg -target /
+
       - name: Upload installer to GitHub Actions
         uses: actions/upload-artifact@v3
         with: