It sounds as though the application doesn’t have access to that location to save images.
Go to your Security and Privacy settings and then select, Full Disk Access then to add Photo AI click the Add button + then select Photo AI in the list, then click Open.
Please open Topaz Photo AI, go to the menu bar on the top and click the Help > Open Log Folder menu option. Attach the logs files that you can see in the window that opens.
It sounds like Topaz Photo AI may be running out of memory to finish writing the upscaled file. I can check the logs to be sure.