Oh yeah - on what your refer to as the "other side" . . . if the browncoat/scratchcoat is in good shape, a finish layer of plaster could be applied over it. FIrst you'd want to apply something like Plasterweld over the surface to ensure adhesive and to prevent the browncoat from sucking moisture out of the finish coat. An alternative to using Plasterweld is damping the browncoat with water before applying the finish plaster. But Plasterweld or a similar product (QuickCrete makes one) would give a superior bond.

Get an electrician to fix the romex. Missenigma is correct that this is currently illegal as hell. In your 5th photo it looks like you have romex buried in skimcoat in a channel as well coming in at a 45º angle.

Anyway, yeah you kind of have a mess. I know how to skimcoat, so I'd be tempted to start patching, but really, it may be easier to just cut everything out to the studs at this point and drywall or put up hardiebacker for tile. You don't need to be particularly good at drywalling if you are going to tile, you can just tape the seams and get a decently flat mud joint to tile over with mortar.

If you want it to look nice and finished for paint, then you will probably want to hire it done. Not really a good "my first time skimcoating" project.

following

@missenigma + @Super Lumen Thank you for the advice! That's really helpful info to know, and thank you for calling out the faulty electrical work! As you mentioned, @Super Lumen, based on the insight here, it may not be the best "my first time skimcoating" project for us, as it's in our kitchen and gets regular foot traffic.

Thank you both for your help here!

Remove the stove. Cover the granite surface with something to protect it.
Carefully remove the wall material since it does not look fixable. If you are not comfortable doing this job, hire a contractor.
Have an electrician look at your whole kitchen and bring everything up to code for safety....whoever did that Romex job may done other things badly.
Check the plumbing and the wall studs and correct or repair whatever you find that is poorly done.
Have a wallboard person install new wall material made for applying tile. Select your backsplash material and have it installed.
It is infuriating when a homeowner trying to improve their property comes upon shoddy work done by a previous owner. The only remedy is to have these issues corrected by someone who knows what they are doing.

Upper cabinets are very often secured to walls with 2 screws at top and screws securing cabinet to cabinet. I'd look into removing them to make it a much easier project.