Detect broken links after publishing page.

[DunklesArchipel]

Checklist

• [x] Added an entry in doc/news/. -> Not required, since no code changes.
• [x] Added a test for this change. -> Not required
• [x] Updated the documentation. -> Not required

The page won't be published until linkchecker is satisfied. We now check links after publishing, which allows fixing the issues in a next step.