Deploy website using GitHub actions (#577)

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### Summary
Deployment of the website using GitHub actions instead of the old method
with a dedicated branch.

Co-authored-by: Frank Harkins <[email protected]>

.github/workflows/deploy-website.yml

@@ -7,8 +7,8 @@ on:
   workflow_dispatch:
 
 jobs:
-  docs_publish:
-      name: Build and publish
+  build_site:
+      name: Build Website
       concurrency: ci-${{ github.ref }}
       runs-on: ubuntu-latest
       steps:
@@ -20,9 +20,25 @@ jobs:
             python-version: '3.9'
         - name: Install tox
           run: python -m pip install -U tox
-        - name: Build Website
+        - name: Build
           run: tox -e website
-        - name: Deploy
-          uses: JamesIves/github-pages-deploy-action@v4
+        - name: Upload Artifacts
+          uses: actions/upload-pages-artifact@v2
           with:
-            folder: website/
+            path: 'website/'
+  deploy:
+    needs: build_site
+    runs-on: ubuntu-latest
+
+    permissions:
+      pages: write
+      id-token: write
+
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+
+    steps:
+      - name: Deploy
+        id: deployment
+        uses: actions/deploy-pages@v2