Issues getting an even plasterboard rebate

I've built a stud framework to block up an internal doorway between two bedrooms.
On one side, I've attached 12.5mm plasterboard but I'm getting a rebate to the existing wall of around 5-6mm at the top and maybe 10-11mm lower down. Was thinking I could take off the 12.5mm and double up 2 sheets of 9.5, but I think then it will stick out beyond the existing wall by around a few mm at the top.

Any ideas what I can do about the varying rebate? Should I just somehow pack out the 12.5mm plasterboard to bring it closer to the existing wall (what can I use for this?) or is there something else I can do?

Wondering if polyprop shims work in this situation?

I’m assuming your stud work is level on one side of the wall but not the other. You could sister up some battens onto the studwork to the correct distance. Wouldn’t use packers behind the plasterboard as it’ll be less supported. Or just use bonding coat to level it up before skimming.