Hello, Lori Harmon.
Welcome to Microsoft Community!
From your description, I think we should have no hardware issues with both Surface Pro 10 and Arzopa USB-C monitor. You have already tested this monitor on another laptop.
So at this point if we're going to continue to investigate this issue, we need to consider the possibility that the cable could be the cause of the problem.
Surface devices have high requirements for cable and accessory compatibility for security purposes. Sometimes the choice of cables can cause similar issues to occur.
Allow me to refer you to the following link which includes specialized accessories and cables for Surface devices. You can choose the corresponding USB-C adapter cable according to your monitor interface model.
Accessories Designed for Surface (microsoft.com)
I would also recommend bringing your Surface Pro 10 with the monitor to a nearby Microsoft site if you want test conditions. I'm sure the staff will be more than happy to provide you with cables as well as a testing environment.
If you're still looking for some system-level advice, then all we can do is manually obtain the driver and firmware installer for the Surface Pro 10:
Download Surface Pro 10 for Business Drivers and Firmware from Official Microsoft Download Center
This can help us update the display related drivers and firmware for better connection performance.
These are some of the ways I can provide you with testing at this time.
Thank you for your support and understanding of Surface products.
Finally, please allow me to express my sincere wishes.
Best Regards.
Leo.L - Microsoft Community Support Specialist