Ability to add non-SMS non-Apple 2FA to an Apple ID?
No, you cannot use TOTP-authentication as implemented by for example Google Authenticator (i.e. RFC6238) with Apple-ID. The only supported system is Apple's own system, which works very similarly to TOTP.

This hasn't got anything to do with the SMS-requirement at all.

As a collary to the above, hardware-based OATH-TOTP solutions such as a YubiKey won't work with Apple-IDs either.