The Steam Machine and Steam Frame are probably delayed, but they still intend to release them in the first half of this year.
They said they planned to have a concrete launch window and pricing by now, but hardware pricing/shortages have made that hard to pin down.
Windows is pretty much the same as Linux, it exposes the raw events from the device and it’s up to the app to handle them. Pretty sure the overlay handles that by sitting between the OS and the game and e.g. translating everything to Xbox style controls if the game needs it (And getting out of the way if it doesn’t)
Outside of that, well Valve added support for the controller to SDL, so anything using it will be fully supported. But then the game needs to actually be using a new enough version of SDL, otherwise it’ll just see a generic controller device, and that can be hit or miss.
Not entirely the same, if the drivers are builtin into the Linux Kernel. I don’t know if the Steam Controller drivers will be Open Source, so maybe its the same.
It definitely looks like it’s going to be a standard USB HID type device, if their SDL support is anything to go by.