Rooms don't always appear in room list results in SSS

Steps to reproduce

Open app
Search for an obscure room
Nothing shows up.
Wait a few minutes
Search again.
Nothing shows up
Wait a few more minutes
Search again
Nothing shows up.

Outcome

What did you expect?

Room list search should work, other than perhaps on the very first bg-roomlist-sync after login. If nothing else, the roomlist cache should remember the existence of older rooms (or do we blow that cache away whenever we launch the app?)
Even if the app is still backpaginating its room list, the user should be told that that is happening: https://github.com/element-hq/element-x-ios/issues/1203

What happened instead?

Rooms were missing from the roomlist and unsure why. This happened on Amandine's account in Berlin; we waited ~10 mins before giving up and switching to legacy to use the room. (I can't remember the room, irritatingly, and it could be that she was killing the app to try to make it sync, before it finished bg-syncing, which might explain why after 10m it still hadn't completed)

Alternatively, perhaps this was an instance of https://github.com/element-hq/synapse/issues/17781 or some other similar SSS bug.

I've tried to reproduce on latest app after a clean start, and it took about 5 minutes to bg-sync older rooms so they'd show up in my room list search results.

Your phone model

No response

Operating system version

No response

Application version

724

Homeserver

No response

Will you send logs?

Yes

element-hq / element-x-ios