Verification between Desktop <> Web takes a few minutes to show emoji

### Steps to reproduce

1. From desktop, go to Settings -> Security & Privacy, then trigger the desktop session to be verified
2. Accept verification request from the web session
3. Start verification process

### Outcome

#### What did you expect?
Next dialogs are quick to load during the verification process

#### What happened instead?
At the point when the emoji should have been shown, the desktop session continued asking me to accept the verification request from another session, while the web session says it's waiting for the desktop session.

After ~5 minutes, the emoji dialogs popped up in both apps.

### Operating system

Arch Linux

### Application version

Element version: 1.10.0

### How did you install the app?

Flatpak

### Homeserver

_No response_

### Will you send logs?

Yes