The problem is that when you add the exe to Steam and run it Proton will create a new fake C-drive for that exe. All your saves are in the fake C-drive for the launcher.
To solve this you can either copy or link the saves to the correct C-drive (it's usually called a Wine or Proton prefix or STEAM_COMPAT_DATA_PATH). Google should tell you how to find the correct folder.
Or you can tell Proton in the Steam-entry to use the prefix of the launcher. You'll have to set STEAM_COMPAT_DATA_PATH to the correct folder. The upside with this approach is that your drive won't be cluttered with useless prefixes for every game.
A third way to handle it is to install games with a helper like Heroic or Lutris, that makes it easier to keep track of the prefixes. They usually have a way to add a game to Steam.