Camera Tracks Character to Limits

This is a sidescroller game, with movement only left and right for the camera, while the player moves up and down as well in the scene.

I’d like to have my camera track my player until the edge of the camera hits the edge of the scene. At that point, I’d like the camera to stop and the player to move on.

Any tips on how I should code this? Maybe have the camera track an empty GameObject instead, or incorporate colliders?

It is worthy to note that I am coding in C#!

First of all there’s nothing like edge of the scene. Its based on the max size of your art. You need to add the checks manually.
Besides that if you want your camera to follow the player then your should keep on updating the camera’s position (with some padding whatever you like) in the LateUpdate() based on the player’s movement.