The Puppeteer is a high-ranking very scary Umichooan man.

He's described as a big, girthy man with eye-searing garish clothes. Most of these things seem to be a rare divergence among umichooans, however current Riung has mentioned him possibly setting it like this himself.

According to Future Riung he might have been the person who granted Victor Vituska the ability to take Gifts from other people.

In session 24, Gaia tried to ask Riung about him. At that exact moment he appeared to ask how does she know of his existance. This might have been foreshadowing that he was watching Riung

In session 26, Claire

In session 26, after part retrieves a tank core with Riungs help, the Puppeteer has revealed that he watched Riung and blackmailed her, expecting to get a favor. Despite almost dying to Gaia and Maelle he convinced Riung to do that, and then he left.

According to Present Riung, he's “someone who can decide our deaths on a whim”.
According to AMANADA, he's a “someone who we can't defeat (yet)”.
According to Gaia, “she will kill him before he can even redeem the favor”.