xmpp user with multiple devices keeps repeating "changed their display name"

**Describe the bug**
I didn't report this at the time, as we can't identify the root cause, but it's now been independently confirmed in a completely different room. You can see from [this public conversation](https://view.matrix.org/room/!qLhNfILESSCaasbRWB:freedombox.emorrp1.name/?anchor=$whmSpvjQNm8FGfQYyFNxoCJ_XxsoN2h5Ky6mlCRC3yk&offset=-29) (and older) that one user keeps rotating between poVoq/kris, when they've tried to set their display name in the ordinary way on the XMPP side.

My guess is that this is actually to do with Presence, and there's something going on with XMPP's equivalent of /away messages, but that's completely unfounded, sorry for the lack of Reproduction steps. Besides, these messages are simply annoying to see constantly in Element clients.

> matrix.org offers an xmpp bridge that you can connect to as any other xmpp MUC. I just got reports that my nick kept cycling between detrout/diane over and over and I'm not really sure why

**Expected behavior**
An XMPP user's preferred display name, when different from their JID should be stable until they manually change it. One workaround that appears to work is for them to set the display name to be equal to their JID user part.

Use the linked public conversation as the symptom reference and investigate the XMPP bridge’s presence and display-name handling for users with multiple devices. Reproduce the repeated changes if possible; done means a preferred name different from the JID user part stays stable until manually changed, including in the reported multi-device case.

Written by the indexing model from the issue text.