build: don't run auto-start-ci on push

PR-URL: #34588
Reviewed-By: Rich Trott <[email protected]>
Reviewed-By: Richard Lau <[email protected]>

Author: mmarchini

.github/workflows/auto-start-ci.yml

@@ -2,7 +2,6 @@
 name: Auto Start CI
 
 on:
-  push:
   schedule:
     # `schedule` event is used instead of `pull_request` because when a
     # `pull_requesst` event is triggered on a PR from a fork, GITHUB_TOKEN will