Split push CI into 2 workflows (#17369)

Co-authored-by: ydshieh <ydshieh@users.noreply.github.com>

.github/workflows/self-push-caller.yml

@@ -0,0 +1,29 @@
+name: Self-hosted runner (push-caller)
+
+on:
+  push:
+    branches:
+      - main
+    paths:
+      - "src/**"
+      - "tests/**"
+      - ".github/**"
+      - "templates/**"
+      - "utils/**"
+
+jobs:
+  run_push_ci:
+    name: Run Push CI
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout transformers
+        uses: actions/checkout@v2
+        with:
+          fetch-depth: 2
+          ssh-key: "${{ secrets.COMMIT_KEY }}"
+
+      - name: Checkout to branch push-ci
+        # A more strict way to make sure`push-ci` is exactly the same as `main` at the push event commit.
+        run: |
+          git checkout -b push-ci
+          git push -u origin push-ci --force

.github/workflows/self-push.yml

@@ -3,7 +3,7 @@ name: Self-hosted runner (push)
 on:
   push:
     branches:
-      - main
+      - push-ci
       - ci_*
       - ci-*
     paths: