var req_item = new Req_shipment.Req_Item() ;
            List<Req_shipment.Req_Item> req_items; req_items = new List<Req_shipment.Req_Item>(); 

                while (sqlResult.Read())
                { i++;
                   req_item.itemIndex = Convert.ToInt32(sqlResult.GetString(2)); req_item.offerId = sqlResult.GetString(3); // Всосали очередную запись 
                   Console.WriteLine($"req_item.itemIndex = {req_item.itemIndex} \t req_item.offerId = {req_item.offerId} "); // Глянули что считали
                   req_items.Add(req_item); // Добавили новую строку в список
                }
 

...
while (sqlResult.Read())
...

            public class Req_shipment
            {
                public class Req_Item
                {
                    public int itemIndex;
                    public string offerId;
                };
                public int shipmentId;
                public List<Req_Item> items;
            };

var req_items = new List<Req_shipment.Req_Item>();

while (sqlResult.Read())
{
    req_items.Add(new Req_shipment.Req_Item { itemIndex = sqlResult.GetString(2), offerId = sqlResult.GetString(3) });
}

var req_items = new List<Req_shipment.Req_Item>();

while (sqlResult.Read())
{
    req_items.Add(new Req_shipment.Req_Item { itemIndex = sqlResult.GetString(2), offerId = sqlResult.GetString(3) });
}