Hi Matthias, I work closely with the documentation team at WRI, and specifically on the PacletTools package.
From your description I see you're using the Workbench plugin to build the documentation. It would help me narrow things down if you could clarify which of the following is the situation you're in:
You've previously built HTML that built and rendered correctly, but recently built HTML has stopped working.
You've previously built notebook documentation, but not HTLM documentation. This is your first time building HTML documentation, but you're seeing problems with the built pages.
In either case, you should know that the documentation building logic in the Workbench plugin recently (earlier this year) went through a major overhaul as part of a concurrent change to bring the ability to author and build documentation into Wolfram Language itself, which greatly improved and modernized the built notebook documentation, but unfortunately caused a few issues with the built HTML documentation.
We're in the process of fixing and updating the HTML generation logic, which should be released alongside the next WL version and as an automatic paclet update.
However, in the meantime, I'd be happy to work with you directly to get you a pre-release version more quickly once it's available. If you're interested in that, please let me know and I will reach out to connect privately.