ci: Run the example notebooks during CI

In the past, we had the issue several times that the capellambse API
would change underneath the example notebooks. This commit reruns the
notebooks during CI to help catch this type of issue more easily.

.github/workflows/code-qa.yml

@@ -93,7 +93,7 @@ jobs:
   pypi:
     name: Publish to PyPI
     runs-on: ubuntu-latest
-    needs: [build, test]
+    needs: [build, test, example-notebooks]
     if: startsWith(github.ref, 'refs/tags/v')
     environment:
       name: pypi
@@ -109,9 +109,32 @@ jobs:
       - name: Publish to PyPI
         uses: pypa/gh-action-pypi-publish@release/v1
 
+  example-notebooks:
+    name: Run and verify the example notebooks
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+      - uses: actions/setup-python@v5
+        with:
+          cache: pip
+          cache-dependency-path: pyproject.toml
+          python-version: "3.12"
+      - name: Upgrade pip
+        run: python -m pip install -U pip
+      - name: Install dependencies
+        run: python -m pip install '.[docs]'
+      - name: Run example notebooks
+        run: |-
+          for file in docs/source/examples/*.ipynb; do
+            jupyter nbconvert --to notebook --execute "$file" --output "$file" --ExecutePreprocessor.timeout "${NOTEBOOK_TIMEOUT_SEC:-300}"
+          done
+
   docs:
     name: Build documentation
     runs-on: ubuntu-latest
+    needs: [example-notebooks]
     permissions:
       contents: write
     steps: