The issue comes down to how the device interacts with your computer. Just like the original version, the new Steam Controller has no native Windows drivers. This means the hardware relies entirely on the Steam app to function properly. If you do not have the game running via Valve’s storefront app, your shiny new gamepad turns into a useless piece of plastic.
Gamers Nexus also reported this and there are a lot of other news outlets also covering this. It is kinda the same as with the steam deck where I noticed that the inputs just don’t work until steam is launched. I really don’t like that I have to have Steam running for this controller to work. I don’t know if it is a dealbreaker for me, yet, but it really put a damper on my enthusiasm about it



OP forgot to quote the actually relevant part which is in an embedded tweet:
The root cause for the problem once again is Microsoft and their locked Xbox / Game Pass eco system.
Valve contributed open source drivers to Linux and SDL months ago.
I said it before and I happily repeat myself again: Just get an 8bitdo controller. The Ultimate2C is affordable and solid (Ultimate 3E for high end users) and I also never encountered a scenario where I would prefer a controller with trackpads over a good wireless keyboard with integrated touchpad and here Framework‘s upcoming one looks the most promising.