Do I need to use a layer of joint compound of spackle I put on drywall damage?

Pictures: https://imgur.com/a/g0kxh4t

The previous tenant had left up a wooden map on the wall that was adhered with extremely strong sticky backings. After removing there was a lot of paint chips and drywall damage.

I’m going to be painting this whole room.

I filled in the wholes with spackle, and sanded. It feels smooth to the touch now. Is it ok that some of the areas where drywall paper was exposed is has slight discolouration (brown tint)? Is it safe to put drywall primer over the damaged area, then do the whole wall with 2 coats? Or should I add another layer of spackle or joint compound over it?