@nicosa23 I had a similar problem.
I don’t know if it is linked to your problem, but it is worth a try.
(Note: I personally have modified the original code slightly to work with our custom theme, so i am not sure if this warnings also occur in the normal plugin)
On PHP 7.4 everything went fine, but switching our server to PHP 8.0 I saw some warnings on the new login url.
Warning: Undefined variable $user_login in /www/wp-login.php on line 1428
Warning: Undefined variable $user_login in /www/wp-login.php on line 1512
Warning: Undefined variable $error in /www/wp-login.php on line 1534
I fixed this by changing the public function wp_loaded().
I added:
$user_login = '';
$error = '';
Before the wp-login is required.
@require_once ABSPATH . 'wp-login.php';
die;
So like this:
$user_login = '';
$error = '';
@require_once ABSPATH . 'wp-login.php';
die;
Maybe this helps you?