ci: deploy the website from GitHub Actions

.github/workflows/update-manual.yml

@@ -1,35 +0,0 @@
-name: Update manual
-on:
-  push:
-    branches:
-    - master
-
-jobs:
-  update-manual:
-    runs-on: macos-13
-    steps:
-    - name: Checkout repository
-      uses: actions/checkout@v4
-      with:
-        # So that we fetch all branches, since we need to checkout the `gh-pages` branch later.
-        fetch-depth: 0
-
-    - name: Install Nix
-      uses: cachix/install-nix-action@v30
-
-    - name: Build manual
-      run: |
-        nix build .#manualHTML
-
-    - name: Push update to manual
-      run: |
-        git checkout gh-pages
-        rm -rf manual
-        cp -R result/share/doc/darwin manual
-        rm result
-        git checkout master -- README.md
-        git config user.name github-actions
-        git config user.email github-actions@github.com
-        git add --all
-        git commit -m "Update manual"
-        git push

.github/workflows/update-website.yml

@@ -0,0 +1,45 @@
+name: Update website
+
+on:
+  push:
+    branches:
+      - master
+
+permissions: {}
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  build:
+    name: Build
+    runs-on: macos-14
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683
+        with:
+          persist-credentials: false
+      - name: Install Nix
+        uses: cachix/install-nix-action@02a151ada4993995686f9ed4f1be7cfbb229e56f
+      - name: Build website
+        run: nix build .#website -o _site
+      - name: Upload website
+        id: deployment
+        uses: actions/upload-pages-artifact@56afc609e74202658d3ffba0e8f6dda462b719fa
+
+  # See: <https://github.com/actions/deploy-pages?tab=readme-ov-file#usage>
+  deploy:
+    name: Deploy
+    needs: build
+    permissions:
+      pages: write
+      id-token: write
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    runs-on: ubuntu-24.04
+    steps:
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@d6db90164ac5ed86f2b6aed7e0febac5b3c0c03e