chore: use built-in GH workflow tasks

.github/workflows/docs.yml

@@ -10,7 +10,7 @@ on:
   workflow_dispatch:
 
 jobs:
-  docs:
+  build:
     permissions:
       contents: write
     runs-on: ubuntu-latest
@@ -34,7 +34,17 @@ jobs:
         run: uv run python tools/build_docs.py docs-build --version latest
         if: github.event_name != 'release'
 
-      - name: Deploy
-        uses: JamesIves/github-pages-deploy-action@v4
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
         with:
-          folder: docs-build
+          path: docs-build/
+  deploy:
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    runs-on: ubuntu-latest
+    needs: build
+    steps:
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4