I have successfully integrated Shopify with Odoo ERP through a connector. Therefore data flows pretty smoothly from Shopify to Odoo and vice versa except for Payment statuses.
Currently, em unable to push the payment statuses such as "Paid" and "Partially" from Odoo to Shopify and it seems like there is no "get" endpoint/API on Shopify that's why em unable to do so. However, It does work for refund payment status.
Please let me know if there is any end point available to get "Paid" and "Partially Paid" status from another platform.