Update Checkout Product Quantity Via Ajax Link

Hello,
we are redesigning our checkout, and we encounter a problem when updating the current quantity of a product in the checkout section.
We would like to use a link for it. We have used this to delete products from the cart.
Delete Link
index.php?dispatch=checkout.delete&cart_id=303560847&redirect_mode=cart

Now we would like to use it for updates from the quantity, but unfortunately it does not work properly.

index.php?dispatch=checkout.update&cart_id=683261860&product_id=697&amount=1&redirect_mode=cart

Here is the target php file where I make my request:

// file: app/controllers/frontend/checkout.php 
// Update products quantity in the cart
//
if ($mode == 'update') {
    if (!empty($_REQUEST['cart_products'])) {
        foreach ($_REQUEST['cart_products'] as $_key => $_data) {
            if (empty($_data['amount']) && !isset($cart['products'][$_key]['extra']['parent'])) {
                fn_delete_cart_product($cart, $_key);
            }
        }
        fn_add_product_to_cart($_REQUEST['cart_products'], $cart, $auth, true);
        fn_save_cart_content($cart, $auth['user_id']);
    }


    unset($cart['product_groups']);


    fn_set_notification('N', __('notice'), __('text_products_updated_successfully'));


    // Recalculate cart when updating the products
    if (!empty($cart['chosen_shipping'])) {
        $cart['calculate_shipping'] = true;
    }
    $cart['recalculate'] = true;


    $_suffix = ".$_REQUEST[redirect_mode]";
}

Does anyone have a tip for me on how I can solve this or what I am missing?

Try to use something like

index.php?dispatch=checkout.update&cart_products[683261860][amount]=1&redirect_mode=cart

(!) Not tested

Thanks it worked, but unfortunately it did not have the expected effect.
It always adds up the number of products and does not set them.