Update Homebrew Tap when releasing

Closes gh-40424

.github/workflows/release.yml

@@ -105,6 +105,20 @@ jobs:
           sdkman-consumer-key: ${{ secrets.SDKMAN_CONSUMER_KEY }}
           sdkman-consumer-token: ${{ secrets.SDKMAN_CONSUMER_TOKEN }}
           spring-boot-version: ${{ needs.build-and-stage-release.outputs.version }}
+  update-homebrew-tap:
+    name: Update Homebrew Tap
+    needs:
+      - build-and-stage-release
+      - sync-to-maven-central
+    runs-on: ubuntu-latest
+    steps:
+      - name: Check Out Code
+        uses: actions/checkout@b4ffde65f46336ab88eb53be808477a3936bae11 # v4.1.1
+      - name: Update Homebrew Tap
+        uses: ./.github/actions/update-homebrew-tap
+        with:
+          spring-boot-version: ${{ needs.build-and-stage-release.outputs.version }}
+          token: ${{ secrets.GH_ACTIONS_REPO_TOKEN }}
   create-github-release:
     name: Create GitHub Release
     needs:
@@ -112,6 +126,7 @@ jobs:
       - promote-release
       - publish-gradle-plugin
       - publish-to-sdkman
+      - update-homebrew-tap
     runs-on: ubuntu-latest
     steps:
       - name: Check Out Code