On Linux, the save data lives in <Steam-folder>/steamapps/compatdata/<AppID>/pfx, where AppID should be 401910.

For some reason, on Windows, the save data lives in the registry.
To get to it, open the builtin utility program RegEdit. There, navigate through HKEY_CURRENT_USER, Software, and E McNeill, where you will see the "folder" Darknet.
Right-click Darknet and export it to a file. Get the file to a new Windows machine however you like, then double-click it, and confirm that you trust where it comes from.

Yes, it is weird. No, I don't know why. Don't ask me. I just managed to dig this up and thought there should be a GUIDE HERE.