Changes to the tab in search changes the tab outside of it

### Steps to reproduce

1. Be on `All`
2. Click on the searchfield
3. Type something
4. Change the Tab to `People`
5. Click on Cancel next to the searchfield
6. You'll now be on `Favourites` instead of `All`

### Outcome

#### What did you expect?

Either no change in the main view or an according change to people

#### What happened instead?

Only the same index of the tab was kept

### Your phone model

iPhone 11

### Operating system version

iOS 16.3.1

### Application version

1.10.2

### Homeserver

matrix.kif.rocks

### Will you send logs?

No

Start by reproducing the search flow on an iPhone or iOS simulator: select All, search, switch to People, then cancel. Trace how the All, People, and Favourites tab state is retained when Cancel is tapped; done means cancelling leaves the main view unchanged or changes it consistently to People.

Written by the indexing model from the issue text.