After having this recur today with a well established Shared Edits + Wiki post, it seems that the problem is definitely the interaction between the two functionalities.
I’ve been using Shared Edits for a while between people with admin privileges without this cropping up. It is only when Wiki is enabled on the same post that we have the problem.
The obvious workaroud is to make all involved category moderators or TL4 so Wiki is not needed, but that has consequences.