Add shipping party to cart

  var shippingParty = new CommerceParty
  {
      Name = Constants.ShippingAddressCommerceName
  };

  var parties = new List<Party> { shippingParty };
  parties.AddRange(cart.Parties.ToList());

  cart.Parties = parties;

  // Always set external id to some magic number (Party in the loaded cart does not contain an ExternalId)
  // the AddShippingInfoToCart processor looks for a ExternalId == PartyId
  shippingParty.ExternalId = Guid.NewGuid().ToString("D");

  var shippingInfo = new CommerceShippingInfo
  {
      ShippingMethodID = request.ShippingMethod.Id,
      ExternalId = request.ShippingMethod.Id,
      PartyID = request.Party?.ExternalId,
      ShippingOptionType = request.ShippingMethod.ShippingOptionType,
      ShippingMethodName = request.ShippingMethod.MethodName
  };

  var request = new global::Sitecore.Commerce.Engine.Connect.Services.Carts.AddShippingInfoRequest(cart,
      new List<ShippingInfo> { shippingInfo }, request.ShippingMethod.ShippingOptionType);

  var result = cartProvider.AddShippingInfo(request);

  if (!result.Success)
  {
      var messages = result.SystemMessages.Select(m => m.Message);
      throw new SystemException(string.Join(",", messages));
  }