actions: re-add prod deployment to update links pr (#356)

Signed-off-by: flakey5 <[email protected]>

Author: flakey5

.github/workflows/update-links.yml

@@ -63,6 +63,13 @@ jobs:
         env:
           GITHUB_TOKEN: ${{ secrets.GH_BOT_TOKEN }}
 
+      - name: Deploy to Production
+        if: steps.git_auto_commit.outputs.changes_detected == 'true'
+        run: |
+          gh workflow run deploy.yml
+        env:
+          GITHUB_TOKEN: ${{ secrets.GH_BOT_TOKEN }}
+
       - name: Alert on Failure
         if: failure() && github.repository == 'nodejs/release-cloudflare-worker'
         uses: rtCamp/action-slack-notify@c33737706dea87cd7784c687dadc9adf1be59990 # 2.3.2