ci: fix examples update workflow

.github/workflows/update-examples-on-release.yml

@@ -6,15 +6,26 @@ on:
 jobs:
   update-examples-pr:
     name: "Update examples PR"
-    needs: [stage, npm-publish]
     runs-on: ubuntu-latest
     steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-node@v4
+        with:
+          node-version: 20
+      - name: Upgrade corepack
+        shell: bash
+        # Forcibly upgrade our available version of corepack.
+        # The bundled version in node 16 has known issues.
+        # Prepends the npm bin dir so that it is always first.
+        run: |
+          npm install --force --global corepack@latest
+          npm config get prefix >> $GITHUB_PATH
       - name: Run upgrade script
-        run: bash ./scripts/update-examples-dep.sh
+        run: bash scripts/update-examples-dep.sh
       - name: Create pull request
         uses: thomaseizinger/create-pull-request@master
         with:
           github_token: ${{ secrets.GITHUB_TOKEN }}
-          head: ${{ needs.stage.outputs.stage-branch }}
+          head: ${{ github.ref }}
           base: main
           title: "release(turborepo): update examples to latest(${{ steps.getVersion.outputs.version }})"