I wonder which authenticator was used in this case (YouTube app). Was it an authenticator that was part of the OS or something else?

I believe the complaint here is that the YouTube app on iOS is an Authenticator for Google Accounts today. I didn't know it was doing anything Passkey-specific on iOS, but that wouldn't shock me given all the other ways it currently is the de facto Authenticator app for your Google Account on iOS today.

Google is basically just using the YouTube app as a second factor.