try deploy the page

.github/workflows/build_docs.yml

@@ -1,11 +1,10 @@
-on:
-  push:
-    branches-ignore:
-  pull_request:
-    branches: [ main ]
+on: [push, pull_request, workflow_dispatch]
 
   # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
+
+permissions:
+  contents: write
 
 env:
   CACHE_NUMBER: 1 # increase to reset cache manually
@@ -52,5 +51,7 @@ jobs:
       - name: Deploy to GitHub Pages
         uses: peaceiris/actions-gh-pages@v3
         with:
+          publish_branch: gh-pages
           github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_dir: ./docs/_build/html
+          publish_dir: ./docs/_build/html
+          force_orphan: true