I can run the login module successfully on iOS 13 but nothing happened when you run on iOS 10. So is it necessary to add "Sign in with Apple" to below iOS 13?
Sign in with Apple is only supported on iOS 13+. In terms of Apple's review guidelines (that state you must support Sign in with Apple if you have other 3rd party login options), so long as it's supported on iOS 13+ and works correctly, you should be good to go.