Currently, there is no formal integration between Square and Siri commands. This would be considered a Feature Request.
I would love to get some extra context from you on how Siri integration with Square Appointments would be helpful for your business - that way I can pass it along to our Product Teams. What did you have in mind?
Real quickly, I’d like to voice command to have Siri read my appts that are scheduled for today/tomorrow, similar to how it works with Google Calendar.