This is probably due to the Flatpak. You have to grant it additional access to the file system using Flatseal (available in the software store) so that it can save files normally. Flatpak packages are containerized and by default are restricted, which tends to cause issues like this.
For reference, here's a screenshot of how that would look like:
You can just enable "All user files" to make it simpler, and restart the application.
Alternatively, you can install this program from another source like Debian package. I'm not familiar with this one though so I don't know which options are there for it in the Zorin OS repositories.
Step 3 in the process is to (optionally) select an output folder. If you do not, the default save is to the same folder as the original. There is no save button. Just check the output folder to see the result.
Edit: Didn't register when posting that you are using Upscaler. This advice applies only to Upscayl.
I've just looked it up and there is not, only Flatpak. You'll have to try installing Flatseal, then, and granting additional file system access to this package.
Also worth noting the author doesn't want to support this app for anything except vanilla GNOME:
This app is intended for GNOME, not for bizarre custom iterations of GNOME.
Another option that you can look into is Upscayl, which is what actually runs behind the scenes of Upscaler anyway. It's an AppImage package, so also non-native, but it runs fine:
Oh, no wait. It's actually available also in other formats, just click on the drop down that says "Alternative Downloads". It has everything.