build: Switch docs workflow to official GitHub actions

.github/workflows/docs.yml

@@ -1,23 +1,18 @@
 name: Documentation
-
 on:
   push:
     branches: [main]
-    paths:
-      - "docs/**"
-      - "aiomqtt/**"
-      - README.md
-      - .github/workflows/docs.yml
   pull_request:
-    paths:
-      - "docs/**"
-      - "aiomqtt/**"
-      - README.md
-      - .github/workflows/docs.yml
-
 jobs:
   docs:
     runs-on: ubuntu-latest
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    permissions:
+      contents: read
+      pages: write
+      id-token: write
     defaults:
       run:
         shell: bash
@@ -43,12 +38,12 @@ jobs:
         run: scripts/setup
       - name: Build documentation
         run: scripts/docs
-      - name: Deploy to GitHub Pages
-        uses: peaceiris/actions-gh-pages@v3
-        if: github.ref == 'refs/heads/main'
+      - name: Upload artifact
+        # if: github.ref == 'refs/heads/main'
+        uses: actions/upload-pages-artifact@v3
         with:
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-          publish_dir: ./docs/_build
-          publish_branch: documentation
-          user_name: "github-actions[bot]"
-          user_email: "github-actions[bot]@users.noreply.github.com"
+          path: docs/_build
+      - name: Deploy to GitHub Pages
+        # if: github.ref == 'refs/heads/main'
+        id: deployment
+        uses: actions/deploy-pages@v4

.github/workflows/publish.yml

@@ -1,20 +1,18 @@
 name: Publish
-
 on:
   release:
     types: [published]
-
 jobs:
   publish:
     runs-on: ubuntu-latest
-    defaults:
-      run:
-        shell: bash
     environment:
       name: pypi
       url: https://pypi.org/project/aiomqtt
     permissions:
       id-token: write
+    defaults:
+      run:
+        shell: bash
     steps:
       - name: Checkout repository
         uses: actions/checkout@v3

.github/workflows/test.yml

@@ -1,10 +1,8 @@
 name: Tests
-
 on:
   push:
     branches: [main]
   pull_request:
-
 jobs:
   test:
     strategy: