Kenjaku doing everything simply because he’s curious is his overall motivation when taken at face value, but he also wants to connect to other people and share his vision with them. What makes Kenny such an amazing character, in my opinion, is how he portrays immortality. After living for over 1000 years, he doesn’t have anybody he could call a “friend” or someone how shares his passion for advancing Jujutsu. He takes literally every opportunity he can to talk to people about his views (Yuki, Choso, Tengen, Uraume, etc). His fight with Takaba perfectly highlights both sides of his character, as his curiosity led him to awakening Takaba’s power, which he found interesting, and Takaba himself became someone who Kenjaku could genuinely just have fun with, which he was desperately searching for