Just checked and it turns out that this is indeed caused by not having enough disk space, not an issue with actual registration. Just freeing up a couple dozen GBs fixed it for me, most of which were just old simulators for versions I didn't really need anymore.
Andreeee
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No scroll support? For a device made by the same brand? Unbelievable, this is just preposterous!
It used to work perfectly fine with iPadOS 13.1 all the way up to 13.3 and they decided to drop support, that's just wrong because me and everyone who used it before 13.4 knows it used to work excellent, "laptop replacement" they said, sure