Thanks for creating the issue.

For reference: we tried in the past and ran into sync issues (something something multiple processes on iOS because of NSE process? can't recall the details), so had to emergency-disable it:

PR disabling it: #2525

Oh my goodness :)
After adding some logs in synapse I can confirm this is why the sync after an app restart is slow on Android.

Could we enable share_pos on the room list here without triggering cross processes dragons ?

If not can we make this an option so that we can store the pos at least on Android in the meantime ?

Could we enable share_pos on the room list here without triggering cross processes dragons ?

I don't know if it's enough to not trigger dragons but it seems like the NotificationClient does not initialize the room list service in multiprocesses mode.

The PR I've listed above disabled it for the encryption sync; we could enable it for the state sync, since the notification client uses a different connection id than the main app.

FYI I've been running a modified version since a couple of days with share_pos on the room-list sliding sync instance and it's a night and day difference.
As expected no trouble on my Android, but I don't have the means to test iOS.