u/fell_over, even on Macs, sometimes an application can freeze and stop responding... i know it sounds impossible... but, even on Macs, that happens from time to time.
In Windows there is a 'task manager' where you can see if the app is still responding... same should be available in the Mac.
If you see that the app is not responding (given your post, seems that the app stopped responding as it stopped copying / synching your data), then you can safely terminate the app, then try again.
u/uniquenamesaredumb, you have warranty on the device you purchased, so take advantage of that, have that unit repaired or swapped for a new one.