Fix deploy: grant write permissions and correct publish_branch input

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

.github/workflows/deploy.yml

@@ -2,6 +2,9 @@ on:
   push:
     branches: [main]
 
+permissions:
+  contents: write
+
 jobs:
   build-deploy:
     runs-on: ubuntu-latest
@@ -32,7 +35,7 @@ jobs:
         uses: peaceiris/actions-gh-pages@v3
         with:
           github_token: ${{ secrets.GITHUB_TOKEN }}
-          github_pages_branch: gh-pages
+          publish_branch: gh-pages
           keep_files: false
           force_orphan: true
           commit_message: Deploy Hugo site