CI: Updated gh pages action deployment (#21)

While publishing the pages from a separate branch is available and marked as classic, use the GitHub Actions upload to Pages directly instead of modifying the branch.

---------

Co-authored-by: Corey White <[email protected]>

Author: cwhite911

.github/workflows/publish.yml

@@ -6,22 +6,38 @@ on:
 name: Quarto Publish
 
 jobs:
-  build-deploy:
-    runs-on: ubuntu-latest
-    permissions:
-      contents: write
-    steps:
-      - name: Check out repository
-        uses: actions/checkout@v4
+  build:
+      runs-on: ubuntu-latest
+      permissions:
+          contents: write
+      steps:
+          - name: Check out repository
+            uses: actions/checkout@v4
+  
+          - name: Set up Quarto
+            uses: quarto-dev/quarto-actions/setup@v2
+            with:
+              version: '1.5.57' # Specify the desired version
+
+          - name: Render Quarto Project
+            uses: quarto-dev/quarto-actions/render@v2
 
-      - name: Set up Quarto
-        uses: quarto-dev/quarto-actions/setup@v2
-        with:
-          version: '1.5.57' # Specify the desired version
+          - name: Upload static files as artifact
+            uses: actions/upload-pages-artifact@v3
+            with:
+              path: docs/
 
-      - name: Render and Publish
-        uses: quarto-dev/quarto-actions/publish@v2
-        with:
-          target: gh-pages
-        env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+  # Deployment job
+  deploy:
+    permissions:
+      id-token: write
+      pages: write
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    runs-on: ubuntu-latest
+    needs: build
+    steps:
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4