iCloud Server communication

iCloud uses an Apple ID as well, and that is the only way to log in with 2 factor authentication on an older device. If you just enter the password or try to enter a password and code together it will either produce an error or loop back. It is advised to enter the password, and then request the code, add the code to the password, and only then hit submit.

When signing into an older device using 2 factor authentication you need to enter the password and code together, and there is a time limit. To make the best use of that time enter the password, then request the code and add it to the end of the password

Get a verification code and sign in with two-factor authentication - Apple Support