try without deploy env

.github/workflows/update-gh-pages.yml → .github/workflows/deploy-github-pages.yml

@@ -8,7 +8,7 @@ on:
 
 jobs:
   build:
-    name: Build and publish
+    name: Build
     runs-on: ubuntu-latest
     steps:
       - name: Set up Node.js
@@ -39,13 +39,11 @@ jobs:
 
   # https://github.com/actions/deploy-pages?tab=readme-ov-file#usage
   deploy:
+    name: Deploy
     needs: build
     permissions:
       pages: write
       id-token: write
-    environment:
-      name: github-pages
-      url: ${{ steps.deployment.outputs.page_url }}
     runs-on: ubuntu-latest
     steps:
       - name: Deploy to GitHub Pages