

I would absolutely not want it to work as a controller outside Steam. In initial mode, aka lizard mode, it works as a keyboard and mouse because they want it to be able to boot your OS. That way you can even use it to manage your UEFI settings. Even in bluetooth mode, the og. SC works initially as a mouse. It’s designed for HTPCs after all.

I didn’t find anything on Valve’s issue tracker with a quick search, but maybe you’d like to investigate deeper.
https://github.com/ValveSoftware/steam-for-linux/issues?q=is%3Aissue+state%3Aopen
You could take a look at game’s logs. For Windows titles, enable logs in Proton by adding PROTON_LOG=1 to launch properties, see README for details.
https://github.com/ValveSoftware/Proton/blob/proton_11.0/README.md#runtime-config-options