Though last I checked no browser had created an API for extensions to implement the passkey API. KeepassXC's implementation for example has to inject JS into every page to override `window.navigator.credentials` ( https://github.com/keepassxreboot/keepassxc-browser/pull/178... ). It works but is brittle, so a proper way through extension API would be nice.
For reference, I just 5 minutes ago opened GitHub in Edge on my iOS device, clicked "Sign in with Passkey", and 1Password correctly popped up and offered to sign in with the passkey I had created in Edge on my desktop. I then opened Safari on my phone, and did the same thing. So it definitely is getting there.
A pure web extension password/passkey manager currently has to go the injection route, and will not surface credentials in native apps. This generally means that if you use such a manager, you need to make not to select any options to remove your password, either from your password manager or from the account behind that native app.