Sorry, I should have made more clear what I mean.
But only for you, I just created a test-account.
When I try to do the same as you now (on Android 13 and Brave browser), then Google password manager pops up and offers me to store the passkey:
This doesn’t seem to happen on your device?! - I personally don’t use Google password manager - thinking of that, I don’t know if I did have to configure something on my Android device, so that it can (and tries) to create passkeys, if by an app or so requested.
By the way, what browser do you use? Chromium-based? [I ask because e.g. Firefox doesn’t have so-called PRF (pseudo-random function) yet, so that you couldn’t create a fully functional passkey for login to Bitwarden “with encryption” because for that, PRF is needed. Chrome and Brave for example do have PRF]