Add push check

Author: haraldng

.github/workflows/push_doc_changes_to_website.yml

@@ -9,7 +9,7 @@ on:
 jobs:
   doc_dispatch:
     runs-on: ubuntu-latest
-    if: ${{ github.event.workflow_run.conclusion == 'success' || github.event_name == 'workflow_dispatch' }}
+    if: ${{ (github.event.workflow_run.conclusion == 'success' && github.event_name == 'push') || github.event_name == 'workflow_dispatch' }}
     steps:
       - name: Set SSH key
         run: echo "$SSH_DEPLOY_KEY" > ssh_deploy_key.pem