Use official auto-merge for repo-sync PRs (#17815)

* Remove automerge label from repo-sync PRs to prevent automerge workflow from kicking in

* Add github-script step to enable GitHub's official auto-merge on repo-sync PRs

* Remove unused variable

Author: JamesMGreene

.github/workflows/repo-sync.yml

@@ -40,7 +40,7 @@ jobs:
           destination_branch: main
           pr_title: 'repo sync'
           pr_body: "This is an automated pull request to sync changes between the public and private repos.\n\n:robot: This pull request should be merged (not squashed) to preserve continuity across repos, so please let a bot do the merging!"
-          pr_label: automerge,autoupdate,automated-reposync-pr
+          pr_label: autoupdate,automated-reposync-pr
           github_token: ${{ secrets.OCTOMERGER_PAT_WITH_REPO_AND_WORKFLOW_SCOPE }}
 
       - name: Find pull request
@@ -88,6 +88,32 @@ jobs:
               console.log(`Branch is already up-to-date`)
             }
 
+      - name: Enable GitHub auto-merge
+        if: ${{ steps.find-pull-request.outputs.number }}
+        uses: actions/github-script@626af12fe9a53dc2972b48385e7fe7dec79145c9
+        with:
+          github-token: ${{ secrets.GITHUB_TOKEN }}
+          script: |
+            const pull = await github.pulls.get({
+              ...context.repo,
+              pull_number: parseInt(${{ steps.find-pull-request.outputs.number }})
+            })
+
+            const pullNodeId = pull.data.node_id
+            console.log(`Pull request GraphQL Node ID: ${pullNodeId}`)
+
+            const mutation = `mutation (id: String!) {
+              enablePullRequestAutoMerge (input: {
+                pullRequestId: $id,
+                mergeMethod: MERGE
+              })
+            }`;
+            const variables = {
+              id: pullNodeId
+            }
+            await github.graphql(mutation, variables)
+            console.log('Auto-merge enabled!')
+
       - name: Send Slack notification if workflow fails
         uses: someimportantcompany/github-actions-slack-message@0b470c14b39da4260ed9e3f9a4f1298a74ccdefd
         if: failure()