CRA: "This lucky item can be part of any set"

I've noticed a few of these CRA "Lucky" items (such as Chaos Von Bon hat or Chaos Vellum hat) and was wondering how the "This lucky item can be part of any set" worked.

If I have a 2 piece CRA (top and bottom) and a 2 piece SW (Weapon and shoes), will my lucky item be part of the CRA set or my SW set?

It assigns itself the the set effect with the highest (or maybe it was lower) set number. I think you'd have to check extractions to figure out what the numbers are.

I YOLO'd and checked, it works with the higher level'd set. Thanks for your help!

Dang, I was hoping it would work for both