Use a different GHA for website deployment

Instead of using `gh-pages` branch for deployment of the website, use
direct deployment with GHA instead. This allows for decoupling of
building (rendering) the site and its deployment, so the workflow
becomes [quarto render -> upload artifact -> deploy artifact] instead of
[quarto publish gh-pages] that never worked inside a container.

.github/workflows/publish.yml

@@ -1,4 +1,4 @@
-name: Render and publish site
+name: Build and deploy site
 
 on:
   workflow_dispatch:
@@ -7,20 +7,39 @@ on:
       - main
       - specky
 
+concurrency:
+  group: pages
+  cancel-in-progress: true
+
 jobs:
-  publish:
+
+  build:
     runs-on: ubuntu-latest
     container: ghcr.io/nbisweden/workshop-reproducible-research/publish:specky
-    permissions:
-      contents: write
     steps:
 
       - name: Checkout
         uses: actions/checkout@v4
 
-      - name: Publish to GitHub Pages
-        uses: quarto-dev/quarto-actions/publish@v2
+      - name: Build website with Quarto
+        uses: quarto-dev/quarto-actions/render@v2
+
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
         with:
-          target: gh-pages
-        env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          path: 'docs/'
+
+  deploy:
+    runs-on: ubuntu-latest
+    needs: build
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    permissions:
+      pages: write
+      id-token: write
+    steps:
+
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4