All you should need to do is to copy/paste over the "world" folder from the previous to the new version. Usually previous saved games will work just fine in newer versions of the game.
You can also copy the moonbase_settings.json if you have any keymapping changes you want to transfer too.
Another convenient way is to use the itch desktop application (which automatically downloads updates as they're released, no manually save-game copying etc!).
Cheers.