Wordpress: custom ajax registration?

Question

WordPress

Good evening everyone!
I ask for help to solve the following problem:
I am writing a plug-in of additional modules for the theme. One of the modules is custom users, written from scratch, as the standard users module in WP does not meet the requirements of the tasks.
I switched to WP not so long ago (I didn’t use ajax before, because I only recently learned a little about it).
So, in the includes folder there is a class that manages all modules and it has a registration handler, this is how adding a hook for an ajax request looks like in the constructor:
$loader->add_action( 'wp_ajax_nopriv_register_ajax_handler, $this, 'register_ajax_handler' );
This is how the register_ajax_handler function looks like:
public function register_ajax_handler {
// Here I just made a test output
echo 'WORK!';
}
In the js file, which is located in js/cmt-plugin.js, there is a handler on the form that checks everything and if everything is ok, then the following script is launched:
var data = {
'action': 'register_ajax_handler'
};
$.post( ajaxurl, data, function( response ) {
$( '.#form-content' ).html( response );
});
}
as a result, in the console it simply gives out that ajaxurl was not found.
I have no idea why this is so, and in general I understand all this at an abstract level so far.
Please tell me what am I doing wrong? My goal is to understand how you can call an ajax request from a class method, something like what I described came out. Thank you.

Answer 1

1. If native users are not suitable, they can do it class My_User extends WP_User
2. Slightly incorrect registration of the action in the OOP format, it is necessary

$loader->add_action( 'wp_ajax_nopriv_register_ajax_handler', array( $this, 'register_ajax_handler') );

3. Check the html code of the page, somewhere inline there should be a script with the definition of the ajaxurl variable
4. And also, there is wp_ajax_nopriv_* and wp_ajax_*
Actually, I think that #2 will solve the problem.