How to make slight Camera move and smooth

So basically I want to make the camera slightly move to sort of look at the mouse, but not look too far so it doesnt move outside the level of my game.

The only game I can think of for an example is Little Nightmares, if anyone has played it or seen it, when you look around you can only look slightly left, right, up, and down. and it smoothly looks around (its kind of like your looking into a doll house)

Im not sure how to make this effect.

Thanks in advance if anyone answers!