I expected something more shocking when I read "working with Russia".
Kagi uses multiple search backends, and of course it needs to forward search terms to these backends. These backends probably can't trace the searches back to the individual Kagi user though, but Yandex could still analyze search trends for example.
What's worse is that - unless they use Yandex' API for free - customers indirectly (and likely unknowingly) support a Russian company with their paid Kagi subscription.
Kagi should at the very least release a statement about this claim.