I'm having exactly the same issue – white main menu and inventory background, which makes text very hard to read and basically makes it impossible to play the game.
OS: Manjaro 22.0
DE: Gnome 43
GPU: Nvidia GTX 1070
GPU Drivers: Nvidia 520.56.06
Kernel: 6.0.6-2-MANJARO
Proton: I've tried Proton Experimental, GE-39 and the latest GE-41.
Game is playable but the videos are not working, there is not even usual typical test-screen place-holder. Tested with Experimental and also with unofficial ProtonGE but there was no difference
steam-1577250-GE-Proton7-43.log
steam-1577250-experimental-bleeding-edge.log
system_info.txt

With current Proton Experimental the videos are now working (both the projector videos in-game and the main menu background). I can't see any remaining problems :tada:
proton experimentalx3 2023-06ge-proton7-43x1 2022-12
Compatibility Report
System Information
I confirm:
steam-1577250.log
Symptoms
There is a vidoe file that is supposed to play as the background of the main menu, inventory, skill menu etc but under Linux it does not plays making most of those menus unusable as visible here:
https://steamcommunity.com/sharedfiles/filedetails/?id=2884297516
https://steamcommunity.com/sharedfiles/filedetails/?id=2884307238
https://steamcommunity.com/sharedfiles/filedetails/?id=2884307194
https://steamcommunity.com/sharedfiles/filedetails/?id=2884307157
Reproduction
Start the game and notice the background of the main menu is missing, you have to progress a bit into the game to open the skill menu but it's perfectly reproducible every time. I have tried Proton GE and other versions, it also happens on my Steam Deck.