ci: auto-trigger homebrew-tap formula update on release

Add an update-homebrew job to the release workflow that dispatches
the update-formula workflow in bpauli/homebrew-tap after GoReleaser
completes. Requires a TAP_GITHUB_TOKEN secret with cross-repo
workflow dispatch permissions.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: bpauli

.github/workflows/release.yml

@@ -44,3 +44,26 @@ jobs:
           args: release --clean --config /tmp/.goreleaser.yaml
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+
+  update-homebrew:
+    needs: goreleaser
+    runs-on: ubuntu-latest
+    steps:
+      - name: Get tag
+        id: tag
+        run: |
+          if [ "${{ github.event_name }}" = "workflow_dispatch" ]; then
+            echo "tag=${{ inputs.tag }}" >> "$GITHUB_OUTPUT"
+          else
+            echo "tag=${GITHUB_REF#refs/tags/}" >> "$GITHUB_OUTPUT"
+          fi
+
+      - name: Trigger homebrew-tap update
+        run: |
+          gh workflow run update-formula.yml \
+            --repo bpauli/homebrew-tap \
+            --field formula=gccli \
+            --field tag=${{ steps.tag.outputs.tag }} \
+            --field repository=bpauli/gccli
+        env:
+          GH_TOKEN: ${{ secrets.TAP_GITHUB_TOKEN }}