Now I noticed another thing, that break sample cannot be changed into groove clip. Other samples used there can. Why is that? I think I am getting closer.....

All right. So what I did was I found the original sample / loop used (in that that Break track you can see in the screenshot) and drag it to a new audio track again, made a groove clip out of it and used that. And after export, everything is great. So I probably somehow imported this sample in a wrong way. Don't know how I did it. So we can close this as solved. Lesson learned...don't rename the sample names used in the track, so you can find the original ones in case you need them in their original form.

Cool. I was out for a few days so didn't see your previous updates. If a clip can't be converted to a Groove Clip, that suggests it's already been stretched with Audiosnap or is another type of tempo-matching loop like REX.