docs: update GitHub Actions workflow to enhance permissions and improve deployment process for GitHub Pages

.github/workflows/build.yaml

@@ -10,7 +10,9 @@ on:
   workflow_dispatch:
 
 permissions:
-  contents: write
+  contents: read
+  pages: write
+  id-token: write
 
 concurrency:
   group: gh-pages
@@ -40,9 +42,16 @@ jobs:
         run: |
           python docs/build_versions.py
 
-      - name: Deploy to gh-pages branch
-        uses: peaceiris/actions-gh-pages@v4
+      - name: Upload Pages artifact
+        uses: actions/upload-pages-artifact@v3
         with:
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_branch: gh-pages
-          publish_dir: site
+          path: site
+
+  deploy:
+    needs: build
+    runs-on: ubuntu-latest
+    environment:
+      name: github-pages
+    steps:
+      - name: Deploy to GitHub Pages
+        uses: actions/deploy-pages@v4