The root problem is that a mouse camera movement only need to happen when mouse itself moves, while gamepad stick camera movement needs to happen every frame regardless if gamepad stick was moved or not, for example if we hold gamepad to the right such as resulting vector would be (1.0f, 0.0f), we still need to move camera to the right every frame even if stick itself is staying fully pressed to the right.

Hence why in the example provided "MouseLook_PlayerInput.LookAround" doesn't quite work, as it's only called when gamepad stick changes its value, and is not called if there is no change in value, hence why you observe camera moving only when stick is moved.

A correct use case would be to invoke this from Update and checking if action is performed, and if it is, moving the camera based on the value.