Hello there, @blossombird.

Thanks for sharing the most detailed information about your concern, and the steps you've taken before reaching us here.

Ideally, applications with an integrated connection should work seamlessly. At this point, it's best to contact the Technical Support team of Square.

With their tools, their specialist can pull up your account information and determine the sync problem. Follow this link for the contact information: Connect Square with QuickBooks Online.

For future reference, you can visit this link to get answers to common questions about the Connect to Square app in QuickBooks. 

You're always welcome here if you have any further concerns. I'm always willing to lend a hand.