To understand Kenjaku's plan, one must first understand why he targeted Tengen. This involves a key triangular relationship: Tengen, the Star Plasma Vessel, and the Six Eyes.
Tengen: Possesses an "immortality" Cursed Technique, but the price is that they periodically "evolve" into a higher-level, non-human existence, which would endanger the barriers they had created to protect Japan. To maintain their human form and sanity, they need to merge with a Star Plasma Vessel to refresh their physical information.
Star Plasma Vessel: A "refresh tool" to maintain Tengen's state.
Six Eyes: Due to some causal connection, whenever the critical period for the Star Plasma Vessel to merge with Tengen approaches, a Six Eyes wielder is bound to be born in the world. One of the reasons for the Six Eyes' existence seems to be ensuring the smooth merging of the Star Plasma Vessel and Tengen, they can be seen as Tengen's "bodyguard."
What does Kenjaku want to do?
He wants to interrupt or even facilitate Tengen's "evolution" to see what spectacular (terrifying) sight would emerge once this immortality technique runs wild and is forcibly linked with all of humanity.
To force Tengen, the immortal sorcerer protecting Japan's barriers, to merge with all of Japan's population, giving birth to an unprecedented Cursed Spirit.
In his eyes, this is likely the peak manifestation of cursed possibilities a great work sufficient to overturn the rules of the world.
But here's the problem: with a bodyguard like the Six Eyes wielder around, it's very difficult for him to succeed.
Historically, Kenjaku tried to stop the Star Plasma Vessel's merger at least twice, but both times he was defeated by the Six Eyes wielder of that era. He realized that on his own, it would be hard to break through the iron triangle of "Six Eyes + Star Plasma Vessel + Tengen."
So, he thought of relying on others. He set his sights on Sukuna, whose strength was unfathomable.
His plan was likely to guide or use Sukuna at his peak to crash through the Six Eyes wielder's protection, interrupt the merger, and force Tengen to "evolve" in an uncontrollable direction.
However, man proposes but God disposes—Gojo Satoru was born.
The Six Eyes wielder of this era was absurdly strong.
After assessment, Kenjaku reached a conclusion that made his teeth ache a bit: even if Sukuna were fully resurrected, he might not necessarily win against Satoru.
Plan A (relying on Sukuna to force his way through) saw its risk increase greatly.
What to do?
Kenjaku remembered his past works and thought about how to enhance Sukuna's strength.
This brings us to Yuji's true origins. Before the Hidden Inventory Arc, Kenjaku possessed the body of Kaori and conceived a child with Jin, giving birth to Yuji for the purpose of creating a "specially-made body" for Sukuna.
This body integrated the technology of the Cursed Womb: Death Paintings, and its soul even has a special connection with Sukuna, making it a perfect vessel that could theoretically maximize Sukuna's power and perhaps even come with some insurance or buffs.
Simply put, Yuji was an enhancement part or a dedicated chassis prepared by Kenjaku to increase Sukuna's combat power after resurrection, thereby increasing the chances of winning against Satoru.
However, the chessboard of fate is always full of surprises.
Just as Kenjaku was adjusting his plan, preparing to use the enhanced Sukuna to clash with the strongest of today, a variable completely outside of causality appeared—Fushiguro Toji, that monster with a Heavenly Restriction, a guy who has zero Cursed Energy and might therefore be overlooked by many arrangements of fate.
Involved in the Star Plasma Vessel incident for money, he actually killed the Star Plasma Vessel of that time, Amanai Riko, in an almost accidental manner.
This act directly flipped the chessboard.
Tengen's merger process was unexpectedly interrupted and fell into an unstable state.
Kenjaku's "Sukuna breakthrough" plan, which he had planned for a long time and pinned great hopes on, lost much of its value before it even began because the target had changed.
But ironically, Kenjaku's luck or sharpness was excessively good.
It was precisely during this incident that he discovered Geto Suguru, who possessed Cursed Spirit Manipulation.
This Cursed Technique had a terrifyingly high upper limit. It was practically a perfect tool custom-made for his ultimate dream of "merging humans and Cursed Spirits" and "exploring cursed possibilities".
For a scientist like Kenjaku, the temptation of a body with "Cursed Spirit Manipulation" that could control countless Cursed Spirits was likely revolutionary.
Thus, a key turning point likely emerged: Kenjaku temporarily abandoned his original plan revolving around Yuji and Sukuna, and instead began to plot with all his might for Suguru's body.
Yuji, the "perfect vessel" carefully prepared for Sukuna, along with Sukuna himself, was set aside by Kenjaku.
But as for any direct relationship with the current Sukuna?
After Kenjaku adjusted his core strategy due to Toji's accident and the discovery of Suguru, the priority of Yuji's body—the "body prepared for Sukuna"—likely dropped significantly in Kenjaku's mind.
After Sukuna's resurrection in Utaha's body, Kenjaku did not immediately go to obtain this "dedicated body."
Therefore, while there are deep design connections and bloodline entanglements between Yuji and Sukuna, they don't have much of a relationship in the current timeline. At most, Yuji and Sukuna just have one more relative.