In case someone else comes across this, I found the problem and the solution. It had nothing to do with the version.
The game is hard-coded to support only a limited amount of saved games (around 100). If you try to go beyond this limit you get a message in-game saying so. In order to save a new game you have to delete old ones.
However, the GOG Galaxy Cloud storage ignores this limit when "syncing", and you can end up with more than the allowed files in the save folder. When the game tries to read the save folder in that condition, it crashes, whether it's to save a new game or to load an old one.
To solve the issue, disable the cloud save syncing and delete the excess save files.
Thanks @jsidhu762 for the suggestions.