Golovkin would have to treat Barkley with respect that's for sure. That said I think the Khazak is just technically so superior that he would have to be favoured in this match. Not saying it would be easy, it wouldn't, but I'd put my cash on GGG.
I agree you can call him a true MW (in the sense that he campaigned there when at his physical peak). Just not an ATG MW.
A prime Barkley was a huge, extremely strong, murderous punching middleweight .. he was also slow starting, hittable and had a solid but not concrete chin .. GGG while still a bit untested is a much tighter, focused, extremely talented hard as nails middleweight who would likely put the Blade out after eating some monster shots ..