We've fixed this as follows, but not sure what caused it.
We made an FTP share to test things. We could write in the Users/<username> folder, but not the Users/<Username>/<serverid>/ folder and below.
The only difference between those folders was an 'Unknown Account' with all privileges unchecked. Looked a bit like a remnant from a system move.
FTP started functioning again by removing this account from the folders, copy the server files somewhere else, and copying them back.
Just removing the account wasn't enough, neither was re-applying privileges recursively, like some privileges were lingering somehow.
No idea what was going on but at least things work again.