[IDP-1845] Fix docs deploy (#21)

.github/workflows/publish-docs.yml

@@ -12,14 +12,8 @@ jobs:
     runs-on: ubuntu-latest
 
     permissions:
-      contents: read
-      pages: write      # to deploy to Pages
-      id-token: write   # to verify the deployment originates from an appropriate source
-
-    environment:
-      name: github-pages
-      url: ${{steps.deployment.outputs.page_url}}
-
+      contents: write  # to update the retype branch
+
     steps:
       - uses: actions/checkout@v4
 
@@ -30,11 +24,6 @@ jobs:
           config: docs/retype.yaml
           license: ${{ secrets.RETYPE_API_KEY }}
 
-      - name: Upload Retype artifact
-        uses: actions/upload-pages-artifact@v2
+      - uses: retypeapp/action-github-pages@latest
         with:
-          path: ${{ steps.retype.outputs.retype-output-path }}
-
-      - name: Deploy to GitHub Pages
-        id: deployment
-        uses: actions/deploy-pages@v4
+          update-branch: true