When not switching to the other account for a while, it stops receiving notifications

### Steps to reproduce

1. Have two accounts
2. Stay on the second account for a while

### Outcome

#### What did you expect?

I have notifications incoming for both accounts

#### What happened instead?

There are no notifications for the other account. When I switch to the other account, the chat list is in some old state, then starting syncing (after like 1-2 seconds of being in that old state) and updates all rooms to the latest state.

### Your phone model

_No response_

### Operating system version

Android 17

### Application version and app store

26.08.0

### Homeserver

_No response_

### Will you send logs?

Yes

### Will you submit a Pull Request?

No

Reproduce the issue with two accounts on Android 17 using application version 26.08.0, leaving the second account active until the first stops receiving notifications. Start by collecting the promised logs around background synchronization and account switching. Done means both accounts continue receiving notifications and the inactive account shows current room state immediately when selected.

Written by the indexing model from the issue text.