In the end, somehow magically reinstalling the MESA drivers helped, I ran these commands:

sudo apt-get remove mesa-utils

sudo apt-get remove libgl1-mesa-dri libgl1-mesa-glx libegl1-mesa libgbm1 mesa-utils

After this command, GNOME crashed for me

sudo apt-get install libgl1-mesa-dri libgl1-mesa-glx libegl1-mesa libgbm1 mesa-utils

It seems like I rebooted here or a little higher, I don't remember exactly

sudo apt install --reinstall gnome-shell

and I rebooted through the gnome login manager that started after this command This somehow triggered the first launch in which FSR was disabled

I spent about 2-3 days to get the game working. The main problem was that versions 9 and 8 of Proton, when resetting the settings to "default settings", included FSR, but with FSR enabled, the game hung on the CDPR logo on the loading screen, deleting UserSettings.Json, the game could not start in any case, because the default settings included FSR

When I accidentally enabled FSR for the 2nd time, it seems that reinstalling Mesa didn't help, but the game worked after reinstalling Nvidia drivers

It is worth saying that the very first time the game launched to the main menu with FSR disabled, I immediately turned it on out of curiosity to see what would happen and it killed 2 days of my time, neither reinstalling the game, nor reinstalling Steam and CompatData, the game continued to launch with default settings in which FSR was enabled