Thanks to the @jason098 from LGD discord who found a solution to the problem with the layout switching and lack of action for some buttons:
1. First, backup Cyberpunk2077.exe.
2. Use this command
echo '2C45C6: EB' | xxd -r - Cyberpunk2077.exe
or change 74 to EB by 0x2C45C6 offset in hex editor

If you previously applied my fix, it seems like it should work, but the best thing to do is to restore the exe from backup

and thanks to the @Saancreed from LGD discord for command.

After updating to 2.0, I would get a controller overlay which made the game significantly less immersive and fun. And crouch-toggle did not work no matter what I did.

This worked to fix everything for me on linux+proton, some community members also confirmed it works on windows too. :)