ci: Fix demo index workflow runs too early when a release is made (#7892)

Fixes #7379

Author: avelad

.github/workflows/demo-version-index.yaml

@@ -9,8 +9,6 @@ on:
     paths:
       - .github/workflows/demo-version-index.yaml
       - app-engine/demo-version-index/**
-  release:
-    types: [published]
   # NOTE: So long as releases are made without a personal access token (PAT),
   # they will not activate this workflow's release trigger.  For now, the
   # schedule trigger will compensate for that by updating the index nightly.

.github/workflows/release-please.yaml

@@ -202,3 +202,8 @@ jobs:
           TAG=${{ needs.release.outputs.tag_name }}
           BRANCH=$(echo "$TAG" | sed -e 's/\.0$/.x/')
           git push origin refs/tags/"$TAG"^{commit}:refs/heads/"$BRANCH"
+
+  update-demo-index:
+    name: Deploy Demo Version Index
+    needs: [appspot]
+    uses: ./.github/workflows/demo-version-index.yaml