[BWA-209] VaultVerificationCodeItem are frozen and not updated after getting back to the app

### Steps To Reproduce

1. Open Authenticator app with some TOTP codes setup.
2. Wait till screen timeout and device lock (ex. 30s).
3. Quickly unlock device (Authenticator will be displayed as it was last app).

### Expected Result

TOTP codes should continue countdown.

### Actual Result

In some edge cases after getting back to the Authenticator app countdown was frozen (ex. on 9s) and refreshed only on next TOTP code change.

### Screenshots or Videos

Sorry, despite my best efforts I wasn't able to record this. This happened twice in my case. I belive quick unlock of device just after screen is locked due to lack of activity is key to reproducing this scenario.

### Additional Context

Authenticator seems to use Flow, and Password Manager seems to use StateFlow. Also Authenticator seems to have with some "artificial" delay to stop upstream flow and can use stale stateIn before all flows emit their values (usage of `combine()`).

### Build Version

2025.10.2

### What server are you connecting to?

US

### Self-host Server Version

_No response_

### Environment Details

- Device: OnePlus 15
- OS: Android 16 (CPH2747_16.0.1.303(EX01))

### Issue Tracking Info

- [x] I understand that work is tracked outside of Github. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.