I've migrated to the new Shopify Fulfillment Orders API. I've downloaded the Fulfillment Orders for an Order, then created a new Fulfillment successfully and updated the tracking information for the Fulfillment successfully.
I've noticed that the shipment_status isn't set yet - I was expecting this to change to something like 'in_transit':
"shipment_status" : null,
"status" : "success",
Does anyone know how to update the shipment_status under the new Fulfillment Orders API?