I'm not even 100% sure at this point, I setup jagex launcher when I was drunk, all I know is that I set it up with backup codes that I never wrote down and don't even have access to the authenticator now.. I have the login and email and everything but just can't do anything at all without an auth code.
I'd suggest attempting to set up a new jagex account and see which authenticators are available, see which ones you already have installed on your phone, and try to reset your password to your auth app. I've had to do that once when I got a new phone and had to reset my google password as I used the google auth app. It was super easy.