Is CT stored in the brain (body) or the soul?

Odd question when the Gojo vs Suk points out where CT is specifically stored in the physical brain but that got me thinking on Sukuna himself and other reincarnated sorcerer being able to use their own CT despite being in a different body. As well as soul swap training. And the whole engraved technique thing.

CT stored wholly in brain: Sukuna wouldnt be able to use his CT while in Yuji/Megumi body without fully reincarnating, same with other reincarnate sorc.

CT stored in the soul as instruction, which then engrave upon the brain as physical pathways in order to use it: then shouldn’t soul swap training also allow CT copying instead of only the universal stuff of RCT and SD? Since its the same condition as Yuji gaining Cleave and Dismantle from Sukuna doing it in his body

CT stored only in the soul: Gojo and Suk brain damages themself for no reason

Actually now that i think abt it how the hell does Kenny and Yuta have access to his host CT then they switch the physical brains around?

Am i stupid and missed sth? Is CT stores in the balls?