After I set up the standard command PROTON_USE_WINED3D=1 %command% for launching, I encountered a screen with artifacts but with sound. However, using PROTON_ENABLE_NVAPI helped, and the game launched, albeit with unstable performance. In solo rooms, the FPS ranged from about 30 to 40. After trying everything I could think of, I started disabling certain features, and turning off fsync did the trick. Once I turned it off, the in-game FPS immediately stabilized at 60, and I didn't experience any more issues after a few test matches. The game is running smoothly and without problems – I'd even say it's much better than on Windows.

I also don't recommend trying Proton versions higher than 7. For example, with Proton GE, all textures and models disappeared except for tanks, and on the experimental version, I was getting no more than 2 FPS. Many people have already noted this, but the best performance seems to come from versions 6 and 7.