I might be wrong but I don't think thats how its working. It sounds like your phone saves a password/key locally and then when you load a website, faceid is use

I might be wrong but I don't think thats how its working. It sounds like your phone saves a password/key locally and then when you load a website, faceid is used by your phone to unlock the keyring and sends the normal password to the website. I'm not sure what the UX is when moving devices though.