Is two-factor sign-in broken?

I’m trying to log into the Epic Games Launcher on a new computer, and while it claims that it’s sending me a login code to my email address (and the address looks correct), that email hasn’t actually showed up.
I seem able to receive other emails in my inbox, and the Spam folder doesn’t have it.

Interestingly, it first asked me for an authenticator app code, but I don’t recall setting that up, and there’s no Epic section in my authenticator app, which I think I would have added such a code to…