Woocommerce: Change shipping class based on cart items shipping class count & free & flat_rate (mix of 3 shipping costs type)

I have 2 shipping classes.
One free shipping.
The other is 6 pieces for 1 piece shipping　(id=43)

add_filter( 'woocommerce_package_rates', 'woocommerce_cool_rates' );
function woocommerce_cool_rates( $rates) {
  if ( ! WC()->cart->is_empty() ) {
    $class_cool = array(43);
    $found = false;
    $item_qty = 0;
    foreach( WC()->cart->get_cart() as $cart_item ){
      $item_shipping_class_id = $cart_item['data']->get_shipping_class_id();
      if( in_array( $item_shipping_class_id, $class_cool) ){
        $found = true;  /* Target shipping class found */
        $item_qty += $cart_item['quantity'];
        $item_quantity = floor(($item_qty + 5) / 6);
      }
    }
  }
  foreach ($rates as $rate_key => $rate) {
    if ($found) {
      $cool_cost = $rates[$rate_key]->cost;
      $new_cost = $cool_cost *   $item_quantity;
      $rates[$rate_key]->cost = $new_cost;
      $rates[$rate_key]->taxes = array();
      $rates[$rate_key]->set_taxes(0);
    }
}
return $rates;
}

This time, we have added a new shipping item.
It is a product of ‘flat_rate’.

However, with the above source, the quantity of the ‘flat_rate’ item cannot be calculated.
Therefore, I wrote the source as follows, but it does not work well.

add_filter( 'woocommerce_package_rates', 'woocommerce_package_rates');
function woocommerce_package_rates( $rates) {
  if ( ! WC()->cart->is_empty() ) {
    $class_cool = array(43);
    $found = false;
    $item_qty = 0;
    foreach( WC()->cart->get_cart() as $cart_item ){
      $item_shipping_class_id = $cart_item['data']->get_shipping_class_id();
      if( in_array( $item_shipping_class_id, $class_cool) ){
        $found = true;  /* Target shipping class found */
        $item_qty += $cart_item['quantity'];
        $item_quantity =  floor(($item_qty + 5) / 6);
      }
    }

  }
  $total_shipping_cost = 0;
  foreach ($rates as $rate_key => $rate) {
    if ($rate->get_method_id() == 43) {
      $cool_cost = $rates[$rate_key]->cost;
      $new_cost = $cool_cost * $item_quantity;
      $rates[$rate_key]->cost = $new_cost;
    } elseif($rate->get_method_id() !== 43) { 
      $total_shipping_cost += $rate->get_cost();
    }
  }
return $rates;
}

Please let me know how this mix of 3 shipping costs works.