In the data sent as part of payment processing (https://shopify.dev/apps/payments/processing-a-payment), the order number is not included.
Is there any way to obtain the order number for a payment request, before processing the payment. Seems quite an omission to make in the data, and for that to be missing seems like it was a deliberate decision.
This means it’s impossible to show the order number in the transaction information in the payment gateway reports, and makes any form of reconciliation between systems for the merchant a lot harder than it should be.