This looks very much like what I have:
https://www.ebay.com/itm/11546350835...EAAOSwSfdizu7-
My thought was that this lock holds the doughnut trim piece in place, but the problem with that reasoning is that the lock moves in-and-out by 1/4" inside the doughnut trim piece, and the doughnut shaped trim piece isn't particularly loose. Maybe I need to pry it off? (That seems a little odd, because I think it wouldn't take much to scratch or bend it, which I'm trying to avoid since I don't know what I'm doing at this stage.)