[PM-35175] App flash when logging in by passkeys

### Steps To Reproduce

1. Unlock Bitwarden
2. On Firefox, go a website that supports logging in by passkeys (I used https://passkeys.io)
3. Register an account and enable logging in by passkeys, try to make it the only account for this website
4. Log out of the website
5. Log in by passkey
6. Pass Android OS's verification (for me it's fingerprint)

### Expected Result

After passing the fingerprint verification on the OS, the website would log me in without further distractions.

### Actual Result

Bitwarden app jumps in and out for a moment before the website can log me in, even though it does not need anything else from me.

### Screenshots or Videos

The first black screen is when I verify my fingerprint since I found no way to capture it.

https://github.com/user-attachments/assets/b811df0d-9b06-4cc9-8c8f-aa718aecb8e2

### Additional Context

Firefox info:

```
149.0.2 (Build #2016153095), 9f0b9889e371a1c81cc665cfce6f53803006ad9b
GV: 149.0.2-20260403140140
AS: 149.0
OS: Android 16
```

### Build Version

2026.3.1 (21415)

### What server are you connecting to?

US

### Self-host Server Version

_No response_

### Environment Details

© Bitwarden Inc. 2015-2026

Version: 2026.3.1 (21415)
📱 samsung SM-S921W 🤖 16@36 📦 prod
🧱 commit: bitwarden/android/release/2026.3-rc49@c2ef20e1ed74a9cba60b19d5849af168629d3756
💻 build source: bitwarden/android/actions/runs/23660459640/attempts/1
🦀 SDK: 2.0.0-5676-14521973
🌩 Server: 2026.3.2 @ US

### 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.