OrderOperationServices should use the Order History endpoints to see historical order data for customers' orders instead of Cart History.
These endpoints are for use with the Commerce front-end, and only support authentication as a customer, not an administrator.
The response from the order history endpoints will contain not only
Order information, but also
ReturnAuthorization information, to provide a full picture of the customer’s history.
See the Order History API spec for request and response details.