When creating a new content type in the content type gallery (tenant-level), there is no "document set content types" in the parent category dropdown:
I'm pretty sure the language aspect is not at play here. What could be wrong?
Ok, I found it myself. I figured out that the content type gallery on tenant level is just another site collection at /sites/contenttypehub (I forgot that it used to be that on prem).
Enabling the document set feature on the content type gallery site collection actually added the "document set" content type.
Does not explain why the other categories are missing though, but the initial problem is fixed.