use GitHub Actions for pages deployment

As noted in the readme of
[peaceiris/actions-gh-pages](https://github.com/peaceiris/actions-gh-pages),
GitHub offers basically the same functionality by themselves. Since the
old version was failing anyway, I thought that reducing dependencies
might be a good idea.

.github/workflows/docs.yml

@@ -1,32 +1,59 @@
 name: Continuous Integration - Docs
 
 on:
+  # Runs on pushes targeting the default branch
   push:
-    branches:
-      - master
+    branches: ["master"]
     paths:
       - .github/workflows/docs.yml
-      - "docs/**"
+      - docs/**
+
+  # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
 
-jobs:
-  deploy:
-    runs-on: ubuntu-18.04
-    steps:
-      - name: Checkout sources
-        uses: actions/checkout@v2
+# Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages
+permissions:
+  contents: read
+  pages: write
+  id-token: write
 
-      - name: Setup mdBook
-        uses: peaceiris/actions-mdbook@v1
-        with:
-          mdbook-version: '0.4.2'
+# Allow only one concurrent deployment, skipping runs queued between the run in-progress and latest queued.
+# However, do NOT cancel in-progress runs as we want to allow these production deployments to complete.
+concurrency:
+  group: "pages"
+  cancel-in-progress: false
 
-      - name: Build book
+jobs:
+  # Build job
+  build:
+    runs-on: ubuntu-latest
+    env:
+      MDBOOK_VERSION: 0.4.21
+    steps:
+      - uses: actions/checkout@v3
+      - name: Install mdBook
+        run: |
+          curl --proto '=https' --tlsv1.2 https://sh.rustup.rs -sSf -y | sh
+          rustup update
+          cargo install --version ${MDBOOK_VERSION} mdbook
+      - name: Setup Pages
+        id: pages
+        uses: actions/configure-pages@v3
+      - name: Build with mdBook
         run: mdbook build ./docs
-
-      - name: Deploy on gh-pages
-        uses: peaceiris/actions-gh-pages@v3
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v2
         with:
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_dir: ./docs/book
-          cname: docs.spotifyd.rs
+          path: ./docs/book
+
+  # Deployment job
+  deploy:
+    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/deploy-pages@v2