CI: limit the on push triggers (#35574)

Since now we have workflow_dispatch, we can trigger a workflow manually in case we don't have an open PR.

Also, remove the custom `ci skip` code; it's supported natively for some time now: https://github.blog/changelog/2021-02-08-github-actions-skip-pull-request-and-push-workflows-with-skip-ci/

.github/workflows/docs.yml

@@ -2,8 +2,8 @@ name: Docs
 
 on:
   push:
-    branches-ignore:
-      - "dependabot/**"
+    branches:
+      - main
   pull_request:
   workflow_dispatch: