Switch deploy to gh-pages branch approach

The deploy-pages@v4 action was stuck in an infinite status polling
loop. Use peaceiris/actions-gh-pages instead, which pushes the built
dist/ output to a gh-pages branch.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: thagler

.github/workflows/deploy.yml

@@ -6,9 +6,7 @@ on:
   workflow_dispatch:
 
 permissions:
-  contents: read
-  pages: write
-  id-token: write
+  contents: write
 
 concurrency:
   group: pages
@@ -17,9 +15,6 @@ concurrency:
 jobs:
   build-and-deploy:
     runs-on: ubuntu-latest
-    environment:
-      name: github-pages
-      url: ${{ steps.deployment.outputs.page_url }}
     steps:
       - uses: actions/checkout@v4
 
@@ -31,10 +26,8 @@ jobs:
       - run: npm ci
       - run: npm run build
 
-      - uses: actions/configure-pages@v5
-      - uses: actions/upload-pages-artifact@v3
+      - name: Deploy to gh-pages branch
+        uses: peaceiris/actions-gh-pages@v4
         with:
-          path: dist
-
-      - id: deployment
-        uses: actions/deploy-pages@v4
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: ./dist