For better and worse, Webauthn is one of the "choose your own adventure" PKI systems where the keys themselves suggest which PKI algorithm/details they use. This is partly because Webauthn has been around a long time and has had to backwards compatibly support a wide variety of physical security keys over the ages.
Most good open source libraries for implementing passkeys will do a good job of limiting passkeys to known good algorithm choices, including any PQ requirements/suggestions. The Passkey standard itself also sets a "higher water" baseline above Webauthn's supported algorithm list.
Also, the same risk applies, but to an even greater degree, with a password.
Little harsh to say I have NO idea what I am talking about, though.
I still don't agree that companies won't revoke their passkeys if we are in a PQ world.
If they don't, you are still in a better place than passwords. Each public/private key pair is unique for every domain, so a compromise in one place is not a compromise in others. Many people re-use passwords (even if you don't).