May be it is not compatible with that setup.
If you cannot make it work with that setup and want a refund please contact using https://www.shamimsplugins.com/contact-us/

As you are using two factor authentication, there is no need to use any captcha.
Captcha block any bot, as you are already using two factor authentication, bot cannot pass that step. So no need to use captcha there. If you want you can use captcha in any other forms, eg. comment, you can use there. In that case deselect login form captcha.

You can disable captcha check from login page. Unchecked Login Form from Dashboard > Settings > Advanced noCaptcha & Invisible Captcha

Add following code in your child theme’s functions.php (untested)

add_filter( 'authenticate', function( $user, $username = '', $password = '' ){
    if ( $user instanceof WP_User ) {
	if ( array_intersect( $user->roles, [ 'administrator' ] ) ) {
		remove_filter( 'authenticate', array( anr_captcha_class::init(), 'login_verify' ), 999, 3 );
	}
    }
    return $user;
}, 990, 3 );

Let me know.

Please follow https://www.shamimsplugins.com/docs/advanced-nocaptcha-recaptcha/troubleshoot-2/license-keys-not-activating-2/