Why are there different cookie sets in wordpress on the page and in ajax?

Question

HTTP Cookies

In wordpress, I wrote cookies in ajax, after which they are correctly displayed in ajax, including after refreshing the page:

add_action('wp_ajax_addtocart', 'addtocart_callback');
add_action('wp_ajax_nopriv_addtocart', 'addtocart_callback');
function addtocart_callback() {

  var_dump($_COOKIE);

  ...
  setcookie('cartQuantity', $cartQuantity, time() + (86400 * 30));
  ...
  wp_die();
}

However, if you just write on the page, for example, in header.php,
var_dump($_COOKIE);
then another cookie set is displayed there, in which there is no cartQuantity.
How to get on page cookies written in ajax?