Message Search done, but no search available on restart search starts to reindex some of the messages

### Steps to reproduce

1. I start Element
2. I see no search option
3. I go to All Settings>Securits & Privacy> and manage search
4. I see that it is not done and that 4 rooms are missing.
5. I wait till it is done
6. I close it with Done.
7. Still no search option at the top where it was in the past on older computers I have owned with Element
8. I quit element.
9. I redo 1-9 a few times and see no change

### Outcome

#### What did you expect?
To see the search icon at the top - and probably not trying to load a few rooms every time.

#### What happened instead?
No search icon at the top - and loading a few rooms every time.


### Operating system

Xubuntz 24.04

### Application version

Element version: 1.11.87 Crypto version: Rust SDK 0.7.2 (517d99b), Vodozemac 0.7.0

### How did you install the app?

https://docs.matrix.kit.edu/en/clients/install_linux/#debianubuntu

### Homeserver

https://matrix.uni-bielefeld.de

### Will you send logs?

Yes