AJAX action not triggering PHP function

The problem is with the AJAX endpoint URL, i.e. url: userimg.ajax_url, which is not actually defined in your JS/PHP code.

More specifically, you did define the correct URL, but in the JS object, the property name is ajaxurl and not ajax_url:

// wrapped for brevity
wp_localize_script( 'ajax-account', 'userimg', array(
  'ajaxurl' => admin_url( 'admin-ajax.php', 'relataive' )
));

So in your $.ajax() args, just make sure you use the correct property name — ajaxurl. Or change the one in your PHP to ajax_url.

And then the problem would be gone.