The right stick of my Xbox One controller responds when turning left or right not immediately, but only if I've moved it a bit further. Does my controller have an error or should it be that way?
The stick likes to break because it is the hardest to use. Then usually starts as described by you.
There's if there's an ELITE controller in the app "Accessories" an area where you can adjust the emprindlichkeit the sticks and trigger. Otherwise, almost only the variant remains to buy a new one.