Can I pass my data through Woocommerce snippets?

Question

WooCommerce

This is the code to remove an item from the cart

add_action('wp_ajax_remove_cart_item', 'remove_cart_item');
add_action('wp_ajax_nopriv_remove_cart_item', 'remove_cart_item');
        
function remove_cart_item() {
  global $woocommerce;
  $cart_id = wc_clean($_POST['cart_id']);

  if(WC()->cart->remove_cart_item($cart_id)) {
    WC_AJAX::get_refreshed_fragments();
  } else {
    $data = array(
      'error' => true
    );
    echo wp_send_json($data);
  }

  wp_die();
}

But the problem is that in order to make the "add to cart" button available, I need to get the product id in the js. I know how to get the product id. The problem is how to pass this id to js. I have only 2 options in my head - make one more request to the server before removing the item from the cart, but this method is not very correct, as for me. And the second - in the woocommerce_add_to_cart_fragments filter, in the fragments, create the product_id key and, when replacing the content of the elements, check for this key. But also not a great option. Is it possible somehow to add one more key to the cart_hash and fragments returned after WC_AJAX::get_refreshed_fragments() only in the function I need?
Addendum: After looking at the code of the method, I came to the conclusion that it might be easier to write my own similar function that will take parameters? I still write all the js code myself.