zako However, when I am creating the passkey and storing it in the google password manager I am asked to provide and set a lock for the phone although the phone already has a lock method.
Yes, it's an infinite loop. Unfortunately I don't think there is a reliable way to use passkeys with Google Password Manager on GrapheneOS. I don't know if Google has set some (to me unknown) conditions as to which operating systems are allowed to use their passkey sync feature. Or it might be something else. Who knows. I did test this a lot a while ago on different devices, and it doesn't seem to have become better. (I did find a workaround then, which was very inconvenient to set up, and would likely have resulted in users being locked out of their passkeys if they ever lost their device).
You can use another app for storing that passkey. Popular passkey managers in this community are Bitwarden and Proton Pass.