I use selfhosted vaultwarden [0] instance (its a rust implementation of the bitwarden server), and the bitwarden apps (i point the apps to use my server instead of bitwarden).
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.
Bitwarden, which you can self-host (I do this) seems to have at least partial support now, and I know they're working on improving it. However, I'm not sure if their client and server are both fully FOSS.