Refactor CI on documentation

.github/workflows/check_doc.yaml

@@ -0,0 +1,63 @@
+name: Check Documentation
+
+on:
+  pull_request:
+    branches:
+      - '*'
+    paths:
+      - '.github/workflows/check_doc.yaml'
+      - 'docs/**'
+
+jobs:
+
+  docs:
+    name: lint, build and verify
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Check out code
+        uses: actions/checkout@v5
+        with:
+          fetch-depth: 0
+
+      - name: Install markdownlint
+        run: |
+          npm install --global markdownlint@0.29.0 markdownlint-cli@0.35.0
+
+      - name: Lint
+        run: ./docs/scripts/lint.sh docs
+
+      - name: Setup python
+        uses: actions/setup-python@v6
+        with:
+          python-version: '3.12'
+          cache: 'pip'
+          cache-dependency-path: "./docs/requirements.txt"
+
+      - name: Build documentation
+        working-directory: ./docs
+        run: |
+          pip install -r requirements.txt
+          mkdocs build --strict
+
+      - name: Setup ruby
+        uses: ruby/setup-ruby@v1
+        with:
+          ruby-version: '3.4'
+
+      - name: Install html-proofer
+        run: |
+          gem install nokogiri --version 1.18.6 --no-document -- --use-system-libraries
+          gem install html-proofer --version 5.0.10 --no-document -- --use-system-libraries
+        env:
+          NOKOGIRI_USE_SYSTEM_LIBRARIES: "true"
+
+      # Comes from https://github.com/gjtorikian/html-proofer?tab=readme-ov-file#caching-with-continuous-integration
+      - name: Cache HTMLProofer
+        uses: actions/cache@v4
+        with:
+          path: tmp/.htmlproofer
+          key: ${{ runner.os }}-htmlproofer
+
+      - name: Verify
+        run: ./docs/scripts/verify.sh docs/site

.github/workflows/check_doc.yml

@@ -1,25 +0,0 @@
-name: Check Documentation
-
-on:
-  pull_request:
-    branches:
-      - '*'
-
-jobs:
-
-  docs:
-    name: Check, verify and build documentation
-    runs-on: ubuntu-latest
-
-    steps:
-      - name: Check out code
-        uses: actions/checkout@v5
-        with:
-          fetch-depth: 0
-
-      - name: Check documentation
-        run: make docs-pull-images docs
-        env:
-          # These variables are not passed to workflows that are triggered by a pull request from a fork.
-          DOCS_VERIFY_SKIP: ${{ vars.DOCS_VERIFY_SKIP }}
-          DOCS_LINT_SKIP: ${{ vars.DOCS_LINT_SKIP }}