Allow me to help share information about syncing or importing transactions from Square to QuickBooks Online (QBO).
As of now importing transactions from Square as sales receipts instead of invoices is not yet available or supported. I understand how important this option/feature on your end and with your business. I'll do take note with this and pass along the suggestions to our product developers/engineers. This way, they'll be aware and might consider the option on the future updates.
On the other hand, you may check this article for additional reference about importing Square transactions to QBO: Sync with Square Hub.
Let me know if you have any other questions about syncing with Square, I'll always be here to help. Have a great day ahead!