Shopware 6 change shipping method programmatically in checkout on order submission

I have two of same shipping methods with different price matrix, depending on customer distance, one of the two shipping method should be selected. This has to be done programmatically on checkout order confirmation, I looked at the cart collector, but it’s about changing price of an item. I didn’t find anything covered in documentation regarding shipping method change.

private function getShippingMethod(string $id, Context $context): ?ShippingMethodEntity
{
    $criteria = new Criteria();
    $criteria->addFilter(new EqualsFilter("id", $id));
    $criteria->setLimit(1);
    $result = $this->shippingMethodRepository->search($criteria, $context);
    return $result->getEntities()->first();
}

public function onOrderValidation(BuildValidationEvent $event)
    {

        ....
   
        $cart = $this->cartService->getCart($this->salesChannelContext->getToken(), $this->salesChannelContext);

        $delivery = $cart->getDeliveries()->first();

        $shippingMethod = $this->getShippingMethod($this->getShippingMethodZoneXId(), $event->getContext());
        $delivery->setshippingMethod($shippingMethod);

}

In the above code I have cart object, and delivery. I get the shipping method which I need to set, but it doesn’t get updated.

Also i need to recalculate shipping price, what is the correct way to do it. any suggestion will be appreciated.