will this work?

.github/workflows/docs.yml

@@ -0,0 +1,36 @@
+name: Push HTML Sphinx documents to gh-pages branch
+
+on:
+  push:
+    branches:
+      - main
+  workflow_dispatch:
+
+jobs:
+  deploy:
+    runs-on: ubuntu-22.04
+    permissions:
+      contents: write
+    concurrency:
+      group: ${{ github.workflow }}-${{ github.ref }}
+    steps:
+      - uses: actions/checkout@v4
+
+      # https://github.com/actions/setup-python
+      - name: Setup Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: '3.10'
+
+      - name: Build
+        run: |
+          pip install -r requirements.txt
+          make html
+
+      # https://github.com/peaceiris/actions-gh-pages
+      - name: Deploy
+        uses: peaceiris/actions-gh-pages@v4
+        if: github.ref == 'refs/heads/main'
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: ./build/html