In a nutshell, you've got the idea. And no: the signed tokens are for all intents and purposes random blobs (often generated literally from /dev/urandom by the server), and the browser strictly associates a WebAuthn keypair to exactly one domain, and no others. Because the browser enforces this, it means it's impossible to phish the user; even if you had the secret key for [email protected] (the music website) you stole from me, you couldn't use it for [email protected] (my bank account).