I think Steam actually primarily catches cheaters by it seeing the other running software rather than looking at the input patterns. I'm not sure whether it would detect a cheat implemented via a camera and custom mouse hardware that sends usb events you didn't do.
But I also think a lot of the hackers in both GTA and CS are cheating in ways that no regular user input could trigger, they're compromising the software at a lower level than that.
From what I know, VAC (Valve Anti Cheat) just looks for processes running on the system and detects injections into CSs memory. Then, for CS:GO specifically there's Overwatch, in which players look at other reported players' gameplay to determine whether they were cheating, and VacNET which is a machine learning system trained on the data from Overwatch to detect aimbots that way. There's a really good talk that someone from valve gave about 3 years ago[0].
The bigger problem is that even with input recognition, one of the biggest problems are wallhacks, meaning you can see other players through walls which is an advantage that's almost as large as aimbotting in tactical shooters like CS.
The comment above was specifically about aimbots, i.e. cheats that mimic a person. Such cheats can be hidden from the system well enough for it to not know there is a program controlling the input. I'm not saying all kinds of cheats can stay 100% undetected and functional with enough effort on the hackers' side, that's obviously false.
But I also think a lot of the hackers in both GTA and CS are cheating in ways that no regular user input could trigger, they're compromising the software at a lower level than that.