Sign in with Apple not working?

Sign-in with Apple is available with participating apps on Apple devices with the latest software—iOS 13 or later, iPadOS 13 or later, watchOS 6 or later, macOS Catalina 10.15 or later, and tvOS 13 or later—and with participating websites in Safari. You can also use Sign in with Apple with other web browsers and on other platforms, like Android or Windows.

If you're using iOS 12.4.6 or lower you'll not be able to sign in/register using the 'Sign in with Apple' option. If you have multiple devices, with iOS 12 and iOS 13, you'll need to do a password reset as outlined here then manually into your account using your private-relay email address as provided by Apple of your Apple ID email address.