Tips for repairing a large, shallow drywall scratch?

All you've done is "Knock the Mud Off". The thin layer of joint compound on the wall.
I would use Spackling and a flat bladed putty knife.
Spackling
Putty Knife

There are plenty of YouTube videos on how to do it.

I would get a small batch of mud and fill in the damaged area. The reason for the mud is it will absorb primer and paint the same as the original wall. After you fill in the damaged area, roll over it lightly with a 3'8" nap paint roller to give it a bit of that orange peel texture that already exists there or dab it with a sponge. You might have to experiment a bit to get it just right but what the heck... Rome wasn't built in a day.

First remove any loose or damaged areas with a utility knife. Cut loose pieces at an angle so as to leave a shallow bevel on the sound wall.

Brush away any loose dust and debris.

Using a wide drywall blade (8-10 inches) or putty knife (4 inches) press fresh joint compound into the damaged wall section using the very tip of the tool in a horizontal swipe.

It may take several swipes (passes) to get the proper results. Ideally you want to slightly over fill the divots and depressions. The compound has a tendency to shrink slightly as it dries espacially for deep cracks.

Let the repair dry over night. Lightly sand the dried epair so that it is level with the surrounding wall. Use your hand to confirm this or a light source held at an angle to the patch will highlight any imperfections.

If needed apply another coat and repeat previous steps.

Prime and paint with 2 finish coats.