Update GitHub Actions permissions and deployment steps

Author: allgandalf

.github/workflows/publish-docs.yml

@@ -17,6 +17,8 @@ on:
 permissions:
   contents: write
   pull-requests: write
+  pages: write
+  id-token: write
 
 jobs:
   build:
@@ -124,6 +126,8 @@ jobs:
 
   deploy-production:
     if: ${{ github.event_name == 'push' && github.ref == 'refs/heads/master' }}
+    permissions:
+      contents: write
     runs-on: ubuntu-latest
     needs: build
     steps:
@@ -140,4 +144,5 @@ jobs:
         uses: JamesIves/github-pages-deploy-action@v4
         with:
           branch: gh-pages
-          folder: site
+          folder: site
+          clean: true