I had the same problem. Tested with multiple replacement dongles sent by Microsoft as replacements. On three different machines. After factory resetting etc. But the Surface App kept on crashing as soon as I put the new dongle into the machine.
Yesterday I managed to download the now unsupported Surface Audio App, and then I could pair the headphones with my new USBLink dongle. After this it works in the "new" Surface App as well. Seems like the Surface App needs fixing.
Downloaded the Surface Audio App via the link provided above. https://www.microsoft.com/en-us/p/surface-audio/9nxjnfwnvm8d?activetab=pivot:regionofsystemrequirementstab
Hope that helps!
J