[Presence] Flicker when using multiple devices simultaneously #15879

I have not seen this in person, but I was informed this is a thing that happens.

From out-of-band

Well, in my case when I implemented a button to set your presence in Nheko, it killed my server, because I had an Element open somewhere and it was flip-flopping between 2 presence states at like 50ms per state

From #9415

Currently I sometimes have 2 clients fighting over presence changes and generating a lot of EDUs in rapid fashing, while some smoothing would be nice. Possibly synapse should just track presence per device and then send the "highest" presence, i.e. busy > online > unavailable > offline.

From #3971 (Although I feel some of this has been mitigated already, it seemed relevant)

An easy way to trigger it is to use the riot-ios app. Just opening the app and then sending it to the background would cause it to hit /_matrix/client/r0/presence/{userId}/status with PUT requests (either updating presence to online or to unavailable.. and after some more inactivity, to offline by a Synapse background task, it seems).
Doing that would cause 100% CPU for a while. I imagine Synapse tries to notify many other servers about the presence change. While this (non-important thing) is going on, Synapse would be slow to respond to other requests.
If I just keep alternating between backgrounding and foregrounding the riot-ios app, I can effectively keep my homeserver at 100% CPU.
Normally though, a few seconds after backgrounding the app (which sets my presence as unavailable), due to a subsequent foregrounding of the app or due to a /sync by another client of mine (on desktop or something), my presence status would change back to online and cause the same thing once again.

CC @nico-famedly

I'm not certain there is a way of reliably testing for this, and there is no guarantees on a video capturing it within the space of a frame(depending on factors such as speed of the system running the server).

It's very possible that fixing #9415 will fix this as well, or at least make it much better.