You will need to post a picture or two showing the wall so we can understand what we are looking at.

Here are a couple pics of the project. That close-up shown in the original post is of the window area next to the drill. I will add corner bead, but the difference in depth is remarkable on that window cut-in. There are also depth differences at various points along the sheetrock replacement areas.

And another closeup looking down towards the floor. The upper piece of sheetrock is the new, the lower piece that is sticking out around that square cut-out is the old with the old paint and texturing over it.

That nasty looking amateur patchwork mishmash is a disaster waiting to happen. Cut out all of the drywall and address the flatness of the studs first by sistering additional support properly. Then properly and thouroughly attach cement backer board with the required fastener schedule, absolutely flat, taping and taping with an alkaline resistant fiberglass and thinsetting the seams. The stone fabricators should use some steel reinforcement channels and a full spread of a high strength thinset like Prolite. No Versabond or any of the cheap box store stuff. No silicone blobs.

The wall should have been padded out before the new drywall was installed, now the backsplash installer will need to shim out the wall.

There's no need to use such nasty terms to discuss my amateur drywall work, GreenDesigns. :) I am an amateur who seems to have somehow gotten stuck with prepping walls for a "Turn-Key" kitchen installer and am already beyond frustrated. The installer's answer to my question is " As long as the surface area that the splash is going to be applied is covered by drywall and as level as possible, this will be acceptable. Just make sure the studs are covered with the drywall and we will handle the rest. After the base cabinets are installed, we will send someone to do a template. The person doing the template will inform our installers of any issues they might encounter so they can be prepared when they show up. IF we need to ensure there needs to be some leveling we will take care of it. All you need to do is install the drywall."

Technically, I have followed their instructions, but the surface level differences gave me pause. I am also concerned about any potential leveling that would need to be done after the cabinets are installed. That, to me, sounds like a disaster. I would rather get it right the first time before cabinets are installed.

Does "sistering additional support" or "padding out" mean shimming? Best product for this? Just good-old wood shims?

I will finish the ends that will show beyond the cabinets and splash but assume that anything behind the cabinets is fine as-is. Yes?

Thanks for the helpful advice, PPF. Did you note the wires coming through for undercabinet outlet strips and wiring? Do I just cut holes and pull those through so that they are at the height that the contractor left them in?

Do I just cut holes and pull those through so that they are at the height that the contractor left them in?

Yes

Just to give you a reference point, when my contractor redid my kitchen, before anything went back in, the walls were taped, floated, finished and painted just as if it was a regular room. Leaving hidden stuff unfinished is lazy work. The bones of your kitchen shouldn't look like Frankenstein!