Think I found the solution! At least – in my case this was the problem:
I created illuminating objects to reflect, which I gave a Compositing tag that hides them to do not appear in the render, only in the reflection. For some reaon this prevents them from appearing in the baked HDRI as well.
So the solution for me was: check the ‘Seen by Camera’ checkbox in the compositing tag.
This is a bug in my opnion, so I will report it to Maxon.
Best,
Jaydude