ci: use action from docusaurus docs

https://docusaurus.io/docs/deployment#triggering-deployment-with-github-actions

.github/workflows/publish-docs.yml

@@ -9,7 +9,7 @@ on:
       - ".github/workflows/publish-docs.yml"
 
 jobs:
-  gh-release:
+  build:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
@@ -18,13 +18,31 @@ jobs:
       - uses: actions/setup-node@v4
         with:
           node-version: 20
+          cache: npm
+
+      - name: cd to docusaurus
+        run: cd docusaurus
+      - name: Install dependencies
+        run: npm ci
       - name: Build
-        run: |
-          cd docusaurus
-          npm ci
-          npm run build
-      - name: Deploy
-        uses: peaceiris/actions-gh-pages@v3
-        with:
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_dir: ./docusaurus/build
+        run: npm run build
+
+  deploy:
+    name: Deploy to GitHub Pages
+    needs: build
+
+    # Grant GITHUB_TOKEN the permissions required to make a Pages deployment
+    permissions:
+      pages: write # to deploy to Pages
+      id-token: write # to verify the deployment originates from an appropriate source
+
+    # Deploy to the github-pages environment
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+
+    runs-on: ubuntu-latest
+    steps:
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4

.github/workflows/test-publish-docs.yaml

@@ -0,0 +1,28 @@
+name: Test deployment
+
+on:
+  pull_request:
+    branches:
+      - main
+    # Review gh actions docs if you want to further define triggers, paths, etc
+    # https://docs.github.com/en/actions/using-workflows/workflow-syntax-for-github-actions#on
+
+jobs:
+  test-deploy:
+    name: Test deployment
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - uses: actions/setup-node@v4
+        with:
+          node-version: 20
+          cache: npm
+
+      - name: cd to docusaurus
+        run: cd docusaurus
+      - name: Install dependencies
+        run: npm ci
+      - name: Test build website
+        run: npm run build