While debugging this "Oh no! Something went wrong" error, we narrowed down the source of the issue: it looks like the current version of the proprietary NVIDIA 580 driver packages cause this error to happen.
Older versions of the proprietary NVIDIA drivers (like 570 and 535) worked fine in our testing, so the upgrade process doesn't result in this error when they're installed. As such, we suspect that there's a regression in the latest proprietary NVIDIA 580 driver that's causing this error, which we hope will be fixed upstream in the near future.
In the meantime, we've since changed the upgrade configs to first automatically remove all NVIDIA 580 driver packages from the system (if present) before performing the Zorin OS 17 to 18 upgrade. This change has been active for at least the past week.
Once the upgrade completes, the user should see a notification to re-install the NVIDIA drivers some time (approx. 5 minutes) after they first log into their newly-upgraded system.