Try an alternative docs GH action

.github/workflows/documentation.yml

@@ -6,15 +6,21 @@ on:
       - main
 
 permissions:
-  contents: write
+  contents: read
+  pages: write
+  id-token: write
+
+concurrency:
+  group: "pages"
+  cancel-in-progress: false
 
 jobs:
   docs:
     runs-on: ubuntu-latest
-    concurrency:
-      group: ${{ github.workflow }}-${{ github.ref }}
     steps:
       - uses: actions/checkout@v4
+      - name: Setup Pages
+        uses: actions/configure-pages@v5
       - uses: actions/setup-python@v5
         with:
           python-version: '3.12'
@@ -23,10 +29,10 @@ jobs:
       - name: Build Sphinx docs
         run: |
           hatch run docs:build
-      - name: Deploy to GitHub Pages
-        uses: peaceiris/actions-gh-pages@v3
-        if: github.ref == 'refs/heads/main'
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
         with:
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_dir: ./docs/build/html
-          force_orphan: true
+          path: './docs/build/html'
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4