Ahhhh. So, you will need to set up your own collection/collections that will have all the information. you would want in it for your orders (who, what did they buy, payment fulfilled, order shipped, etc)
Then when completing different tasks with your API you can also update your tables. Like say a payment is received, update your fulfillment collection to say paid/unfulfilled or something like that.
Definitely make sure to read where to put all your logic for payments and how to secure your collections so that any payment info is secure.
Definitely more work this way, but I’m sure you can make it happen. If it were me, I would start by thinking about your data structure first. What is all the information you will need to capture and how do you want to organize it. Then work on hooking up the API calls for payments so that they update your collections and send your notifications accordingly.