If it doesn't update you can force-update the app by using the installer from gog.com/galaxy.
Let us know if it worked :)
So, I decided to install 126.96.36.199 manually...
It doesn't work on Windows 7 as mentioned, but
it also doesn't work on my Windows 10 laptop. There isn't even an error message, it just won't start.
Maybe some kind of "redist" is missing? Could you please provide me with a complete list of third-party software required for GOG Galaxy to function properly (vcredist, etc.)