Savegame error 116, 304

Errors 116 and 304 are both problems loading the story. 
Can you load the save(s) from the main menu? If you have earlier saves, can they be loaded / reloaded without giving these errors? If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin Enhanced Edition and select Properties, then switch to the Updates tab and check the Steam Cloud section). 
Next, try browsing to the 'Larian Studios' folder in your home directory and rename the 'Divinity Original Sin Enhanced Edition' subfolder. This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Linux user account would effectively do the same thing. With Steam cloud support enabled, Steam would just download the cloud copy of your existing profile. 
After that, start D:OS EE, and create a new profile. Check if you can start a new game and save/load. If that works, exit and copy a couple saves from the renamed folder into the newly created profile's savegames_patch folder folder. If the saves can be loaded/reloaded, move the rest of the saves over. 
If a new profile doesn't help, delete the new D:OS EE folder and rename the original back again.