One workflow I can see it working is square functions on its own out of the box. Make a bot that pulls the reciept data anytime a sale is made and the pos nostr client sends a note to the internal inventory relay. That relay then broadcasts the note to a back end inventory client. A bot pulls the data and adjusts inventory in the database. This connects square to your custom inventory system on nostr rails.
Above works for fiat payments. For lightning payments:
Use the square terminal to ring up the sale as above but instead designate some sort of "other payment" method.
Then create a UI on a separate terminal where you can reference the square transaction. Produce an invoice. Its easy enough for this step to be manual but bonus points if it can detect automatically via bot and automatically create an invoice. When the invoice is paid, auto zap 1 sat to the note to validate payment was made.
This makes it easy to reconcile the number of "other payments" in square against the number of zap transactions in your lightning wallet and the day's lightning balance on your pos client's notes. Double bonus points for creating a bot that auto adds the totals from all the notes with 1 sat zaps, adds up the total value and reconciles that against the number of and total value of "other payment" transactions in square. Also reconciles that against the total daily change in wallet balance. And finally it spits out a closing report with this data. It can even write as a note to a management relay which sends to the management client.