Do you know if there an open source self-hosted implementation available?
Vaultwarden + bitwarden client apps (for desktop/browsers) have passkey support, and i've been using them for a month or two without any issues.
That being said, bitwarden client apps for android and ios are going through a rewrite (from xamarin to native iirc), and are yet to support passkeys. However, the bitwarden folk said passkeys are the next feature coming to these apps.
https://github.com/bitwarden/server
Like the other commenter mentioned, vault warden is the independent server version that doesn't require any of that.