Followed a workaround by hornerwl ( https://github.com/ValveSoftware/Proton/issues/1048#issuecomment-417875072 )

Game ID for CS2 is 748490, not 538680 (of CS1), so that's the difference.

Within winecfg settings, I set the system to Windows 10. I am not sure if making it as Windows 7 would make a difference.

Despite the comment in github, configuration tool works at launch, at least in my environment.

This even worked finte with DualShock 4 via bluetooth.

Very rare freeze (happened once in ten hours+ of play time) Auto save does not appear to be working, so save often manually!