> — never give out codes sent to use via sms or push notifications to someone requesting them via phone or email. Never. The messages often even say that!

I tried making this point downthread but it bears repeating higher up. Per OP, this was account with Authenticator enabled. If you have a working authenticator setup, they aren't going to "ask for a code", since by definition you're already authenticated. And while I'm no expert, I really don't think there is such a thing. Recovery for a lost account never goes back to device-in-hand once you have enabled full 2FA.

Something is being skipped in the description of the phish here. I don't think OP is being completely honest.