Start looking for a new job, OP. I've had a supervisor like this. She was driven by self-interest and wholly embraced her superiority relative to others. Not a good supervisor by any standards. You will just be a number to her, an obstacle to be removed or a pawn to advance her own agenda. Appealing to her boss won't do much, unless you are asked for feedback directly.
In my situation, our boss and HR got involved because she was a dumpster fire, while holding everyone else to a high standard. But they weren't getting rid of her, just requiring retakes of basic supervisory training, a 360 review, and lots of mentoring. I left.