Sync is slow when device notifications are disabled

### Steps to reproduce

1. Login to Element and set device notifications on
2. Leave your phone aside for a couple of days
3. Open the app
4. Now disable device notifications
5. Leave your phone aside for a couple of days
6. Open the app

### Outcome

#### What did you expect?

For step 3 and step 6 to take the exact same amount of time

#### What happened instead?

- Step 3 took a matter of seconds
- Step 6 took multiple minutes

### Your phone model

iPhone

### Operating system version

iOS 15.4

### Application version

1.8.8

### Homeserver

matrix.org

### Will you send logs?

No

### Extra context

Same issue exists for Android too https://github.com/vector-im/element-android/issues/5634

No source files, tests, or entry points are named. Start by reproducing the comparison on iOS 15.4 with Element 1.8.8, using device notifications enabled and disabled after the same idle period, then trace the sync path and measure the difference. Done means the disabled-notification case no longer takes multiple minutes compared with the enabled case.

Written by the indexing model from the issue text.