Question about Yuji and Sukuna cursed techniques

How come Sukuna doesn't have blood manipulation

This could be a case of jjk fans vs reading the manga, but I cannot recall whether this was ever explained. Gojo stated that Sukuna remained in Yuji long enough for shrine to become engraved in him, so shouldn’t the same logic apply to Sukuna? He was inside Yuji long enough that he should have been able to learn Blood Manipulation, or at least know a basic form of it. Fairness Yuji did fully awaken it during the Gojo vs Sukuna fight so maybe it wasn't unlocked yet

Additionally, all of Yuji’s brothers possess some form of Blood Manipulation, so wouldn’t Yuji have had some partially awakened version of the technique from the beginning?

I mean i don't even see a reason for Sukuna to ever use blood manipulation so he could've had it and just not shown the use of it.