Looking for the magic bullet.
Hard to say, I certainly would not go to simply blaming specific makers of parts yet, you haven't put out good build info yet. Was block honed for rings? Was wall wear still within spec, if too loose reringing is worthless. New rings on too loose wall can make motor oil worse. Cannot tell clearly from post, either piston rings or pistons AND rings changed, which is it? Was there ring ridge at top of cylinder and that removed? If not then new rings and even worse different pistons with rings in different place now smacking rings into ridge edge and broken ring already. Any dents or dings in cylinder wall from the previous piston breakup? If vehicle has a good cat then it can run great and burn quite a bit of oil before showing smoke.
You don't say how long motor has been back together but if for a little while sometimes the valve seal rubber quality is not the best even in kits where everything else is good. I've seen seals cook hard to leak oil in as little as 2-3 months if not good ones.