The phone client just knows how to sign + publish notes. You could manage multiple keys there. Could be used to prove identity as well. A site can just present you with a challenge, and you sign the note on your phone and send it to a relay or API endpoint. Rather than an oauth like flow (oauth is clunky) it's more of a 2FA flow. Relying on browser extensions to handle nsec is a terrible experience.
You don't have to rely on an extension any more - there is remote key access protocol nip46, try nsec.app as one implementation. There is Amber offline signer for Android, not sure if it plans/supports QR codes though.
Yeah seems like amber is what I'm thinking. Nip-46 seems needlessly complicated though. You can do so much with it, but the up front setup cost of something like an nsec bunker for the average person is a lot.