WooCommerce: Update shipping costs on checkout using ajax

woocommerce_update_shipping_costs.php

<script type="text/javascript">
  /* in order to update info on your checkout page you need to trigger update_checkout function
     so add this in your javascript file for your theme or plugin
  */
  
  jQuery('body').trigger('update_checkout');
  
  /* what this does is update the order review table but what it doesn't do is update shipping costs;
     the calculate_shipping function of your shipping class will not be called again;
     so if you were like me and you made a shipping method plugin and you had to change costs based on payment method then
     this is the only way to ensure it does just that
  */
</script>

<?php
# add this in your plugin file and that's it, the calculate_shipping method of your shipping plugin class will be called again
function action_woocommerce_checkout_update_order_review($array, $int)
{
    WC()->cart->calculate_shipping();
    return;
}
add_action('woocommerce_checkout_update_order_review', 'action_woocommerce_checkout_update_order_review', 10, 2);
?>

Thanks @PhongGCS, it really works.