I don't think there is much cause for worry that Kagi themselves might use the data for anything bad BUT data leaks do happen and more importantly Kagi will need to play ball with whatever government that exists in the markets they want to have users in, be it the USA but also China, Russia or whatever.

We already know that Google is in fact cooperating with these entities. Not only by giving out user data but also by actively censoring certain things. So there is a precedent.