Existing session suddenly wants to migrate from Classic

### Steps to reproduce

Opening this issue on behalf of a friend

1. Already be using EXA happily while Classic is also on the same device
2. One day, EXA wants me to "Enable your key storage before proceeding to Element X"
3. Open Element Classic
4. Classic says the key backup is set up and working fine

### Outcome

#### What did you expect?
Classic and X agree about the validity of the key backup

#### What happened instead?

### Your phone model

some tablet

### Operating system version

_No response_

### Application version and app store

26.08.0

### Homeserver

fachschaften.org synapse

### Will you send logs?

No

### Will you submit a Pull Request?

No

Reproduce on an Android device with Element X and Element Classic installed, using the reported 26.08.0 setup and the same homeserver. Compare the key-backup state reported by both apps and determine why X requests migration when Classic reports backup as working; done when both apps agree about the backup validity.

Written by the indexing model from the issue text.