Bitwarden not popping up for passkey creation/sign-in

### Origin

Native Application (non-browser app)

### Web URL or App name

webauthn.io

### Passkey Action

- [x] Creating new passkey (Registration)
- [x] Signing in (Authentication)

### Build Information

© Bitwarden Inc. 2015-2025

Version: 2025.6.1 (20398)
📱 google Pixel 8 🤖 16@36 📦 prod
🧱 commit: bitwarden/android/release/hotfix-v2025.6.0-bwpm@e8878d321546a846909c70c00cdf8d7071f0ecf0
💻 build source: bitwarden/android/actions/runs/15984517798/attempts/1

### Additional Information

Although Bitwarden is set as preferred service in "Passwords, passkeys and accounts" and the additional services are disabled, when trying to signup or login in webauthn.io or any other website that supports passkeys, the default Google manager popup is shown. This is happening on both Firefox 140.0.3 and Edge 138.0.3351.66. All the other functionalities, like password autofill, work as expected.

Setting the preferred service to None and then back to Bitwarden fixes the passkey issue temporarily, but the same issue reappears after some (undetermined) time.

### 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.