Ziggurat on Steam supports cloud saves, but on GOG, despite also having cloud saves capability, it does not. Which is very annoying, especially since the game is meant for endless playback and it's nice to have data saved and synced across computers.

There is a way to do this manually. Not optimal, but it works.

I got a new computer and am getting rid of my old computer, so I wanted to move my game progress... What a pain, but I found out how. The save data is located in C:\Users\ {user name} \App Data\Local Low\Milkstone Studios

By the way, you MUST go into folder options and click "show hidden folders" in order to find the folder "App Data."
To do so go to you Windows 10 search bar, (usually at the bottom left of your screen) and type "folder options." There is a button on one of the tabs that you can click to show hidden folders.

Hope this helps someone.