Update: with the last build of the game (#6620276) the problem was solved! 🎉 @kisak-valve should I close this issue or it's better to keep it open for future use?

It seems it was a problem not involved with Proton but with the game's ability to save progress in the Steam cloud: https://store.steampowered.com/news/app/508440/view/3059610062011455972

Compatibility Report

• Name of the game with compatibility issues: Totally Accurate Battle Simulator
• Steam AppID of the game: 508440

System Information

• GPU: NVIDIA GeForce RTX 2070 SUPER
• Driver/LLVM version: NVIDIA 520.56.06
• Kernel version: 6.0.8-arch1-1
• Link to full system information report as Gist:
• Proton version: Proton Experimental / Proton GE 7-41

I confirm:

• [Y] that I haven't found an existing compatibility report for this game.
• [Y] that I have checked whether there are updates for my system available.

Symptoms

Game can't read or write to its root folder (partiatly)

When saving created units/faction/map in editor, game should write them to <game>/TotallyAccurateBattleSimulator_Data/CustomContent/ with folder based on type of their type

• Units -> CustomContent/CustomUnits
• Factions -> CustomContent/CustomFaction
• Maps -> CustomContent/CustomMaps

But for some reason, after hitting the button "Save", the game doesn't create local files.

https://user-images.githubusercontent.com/47672780/202067988-cfa242df-5324-4573-9015-ee0a8cb66416.mp4

Also, I've created map/unit/faction from Windows for testing and had some issues with them on Linux,

• Can't load map for editing/play

• Local units don't have preview images

• And maps too

Additionally, TABS doesn't see templates for map editor.
Without them, you can't create any map

Logs

Proton log
Game log

Reproduction

• Try to create unit/faction
• See that game didn't create them

OR

• Try to create map
• Game doesn't see map templates, and you can't create any map