Update action to deploy to GitHub pages

This is an attempt to fix the permissions error on the last merge.
The code is inspired from https://github.com/actions/upload-pages-artifact

.github/workflows/deploy_docs.yml

@@ -5,46 +5,36 @@ on:
     branches: [ main ]
   pull_request:
 
-permissions:
-  contents: write
-
 jobs:
-  build-and-deploy-docs:
+  build:
     runs-on: ubuntu-latest
     env:
       docs-directory: /home/runner/work/kokkos-core-wiki/kokkos-core-wiki/docs
-      python-version: '3.10'
-    permissions:
-      contents: write
 
     steps:
-      - uses: actions/checkout@v3
-      - name: Set up Python ${{ env.python-version }}
-        uses: actions/setup-python@v4
+      - uses: actions/[email protected]
+      - uses: actions/[email protected]
         with:
-          python-version: ${{ env.python-version }}
-          architecture: 'x64'
-      - name: Install Python dependencies
-        run: |
-          pip3 install -r build_requirements.txt
+          python-version: '3.10'
+      - run: pip install -r build_requirements.txt
       - name: Build documentation
         working-directory: ${{ env.docs-directory }}
         run: |
           make html
-      - name: Archivei documentation
-        uses: actions/upload-artifact@v4
+      - name: Updload documentation as artifact
+        id: deployment
+        uses: actions/[email protected]
         with:
-          name: documentation.tar.gz
           path: ${{ env.docs-directory }}/generated_docs
-      # .nojekyll file is needed for GitHub Pages to know it's getting a ready webpage
-      # and there is no need to generate anything
-      - name: Generate nojekyll file
-        working-directory: ${{ env.docs-directory }}/generated_docs
-        run: touch .nojekyll
-      # This action moves the content of `generated_docs` to the `deploy-doc-site` branch
-      - name: Deploy docs
-        uses: JamesIves/github-pages-deploy-action@v4
-        with:
-          branch: deploy-doc-site
-          folder: ${{ env.docs-directory }}/generated_docs
-          clean: true
+
+  deploy:
+    if: ${{ github.ref == 'refs/heads/main' }}
+    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/[email protected]