Linux

Kind of. It's the Linux kernel that manages all of the controller drivers and makes them available to userspace, mostly via the evdev interface. SDL is a library for managing graphics, sounds and events in a generic way on multiple platforms and devices. It's overwhelmingly the most common library used for Linux games - Steam used it for all of their Linux-native ports of Source engine games, for instance. But it also presents all gamepad events in a consistent way regardless of their "true source", so generic devices tend to work with every game.

SDL3 mostly clears out all the clutter from the previous versions of SDL. It's a mature library and gamedev has come a long way in that time. Getting rid of all the weird stuff that the API accumulated makes it easier to use and maintain. Plus there were things like managing audio generally, and pen-and-touch gestures mobile phones and tablets, that were quite the head-scratchers before. That's all a bit easier now.