Were Otsutsuki that have transcended physical death by passing their Chakra through humans converted into their new bodies modified with Ninja tech, in a way similar to Orochimaru. They could be like the Elf Tribe from Black Clover in those terms.
That would be a nice plot twist, but even though the Kara seems to have some relation to the Otsutsuki, the way they talked about Momoshiki seemed like the Otsutsukis' plans differ from their own.
Because they're now a separate entity from the main family;
My hypothesis is that the Kara were members of the ancient Otsutsuki clan that accompanied Kaguya to Earth, but were against her decision to betray the clan and fought back resulting in their physical deaths. But because of their powerful Chakra they possessed the bodies of nearby deceased humans, yet are unable keep them from decaying thus the need to swap different bodies every often. They would later learn to compensate that by modifying their donor bodies on a genetic basis using Shinobi-Ware they developed over centuries.
Which leads me to my second fan theory: that Kashin Koji is actually an Otsutsuki possessing the body of the late Jiraiya (which he had modified beyond resembling the latter, but has access to his memories and therefore his techniques)
i hardly doubt Kara members are Otsutsuki clan members because they would have to show some features to symbolize themselves as Otsutsuki but sadly i read the manga and didnt see any.....also Jiraiya died at bottom of lake so theres no chance of his corpse re-surfacing for past decade
Letting aside their origins, which we can't speculate nothing yet about, their goal may be finding vessels in order to preserve their conscences through time.
More simple, they are looking for a body-replacement for Jigen, who is not an ordinary man but is on the verge of death, just like the time Orochimaru can stay in a body before replacing it. 'Karma' could be a test to see if Kawaki's body can support Jigen's will and power, just like Orochimaru tested candidates with his Curse Seal.
Naturally, this would mean that even Boruto is a possible candidate, if not for Jigen, for Momoshiki's soul. By Jigen's words, it would be the more accurate possibility.
However, for the path this arc is leading into, it would not be more different from when Orochimaru tried to take control of Sasuke's body. In the end, Jigen will be destroyed by Kawaki or Boruto in his try to take possess on one of the two boys.
Or, even more difficult, the Kawaki we saw at the beginning, the one in the future vs Boruto, is Jigen inside Kawaki's body, but I don't think Kawaki will lose in a confront of will with Jigen, not after Naruto's training.