Linux Gaming

you have two problems here:

• save and config files of linux native games. They will usually create a directory somewhere in your home directory - usually under .var or .config
• and then the save and config files for wine enabled games. They are saved in the steamapps/compatdata directory tree together with all the (windows) files wine needs to run the program. One folder for each game.
  you would need a separate compatdata structure for every steam account to keep the saves separated.
  A possible solution would be to create a start script for every steam user that links the respective folder to compatdata, and then starts steam with the correct credentials.
  You may need to separate other folders too, although I am not sure which those may be. Steam itself can do several users, since it's based on the same code as on Windows. So you may just test with swapping the compatdata folder and check what it's doing.

A funny thing: Proton/wine seems to have a mechanic to provide a username. Because on my games installed by Heroic Launcher i find the windows Profile folder (in the Heroic prefixes folder which is equal to steams compatdata) under "c:\Users[Linuxusername]" while in the steam compatdata the folder is just named "c:\Users\user"
I found that out because I recently copied my saves files from some games that are not cloud- saved to their folders.
but I haven't seen a setting in Steam to use different profile folders in Proton. Which means you will most probably break cloud features when trying to enforce this by start parameters.