https://developer.apple.com/apple-id/
Your Apple ID currently has two-step verification turned on, but two-factor authentication is required. After you turn on two-factor authentication, signing in to your developer account will require both your password and access to your trusted devices or trusted phone number.
How to make this 2-step auth?.. I was trying to login, and it didn't ask me to put SMS code or something else.
It means, "signing in to your developer account will require both your password and access to your trusted devices or trusted phone number" never happened.
In the same time it does ask 2-step auth on https://appleid.apple.com/.
What's wrong?