Migrate fully to GitHub Actions for Pages deployment

Legacy deploy environments (including simply having something in
gh-pages!) is deprecated.

GitHub really wants us to use their deploy-pages system for this, so
switch to it.

.github/workflows/publish.yml

@@ -0,0 +1,31 @@
+name: Deploy site
+
+on:
+  push:
+    branches: [ master ]
+  workflow_dispatch:
+
+jobs:
+  deploy:
+    environment:
+      name: github-pages
+      url: $
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Configure GitHub Pages
+        uses: actions/configure-pages@v5
+
+      - name: Setup deployment
+        run: |
+          mkdir _site
+          cp -r docs translations index.html _site
+
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
+
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4