How do I make my camera scroll and give it like a 0.5 second delay as the player moves for it to catch up?

First of all, it would be helpful if you provided a link to a shared version of whatever project you are working on that requires this feature, so anyone who tries to help has the full information as to where it's at!
Secondly, if you already have a “standard” scrolling script implemented, people will typically do this instead of the just setting the camera to the target:

change [CAM X v] by (((TARGET X) - (CAM X)) / (4)) //using bigger numbers instead of the 4 will make it delay longer; just make sure you don't use a number smaller than 1
change [CAM Y v] by (((TARGET Y) - (CAM Y)) / (4))