Is there any sensible explanation why Kagi does funding Yandex? It seems weird to me.
Legally, Kagi can buy access to Yandex' API. Whether they should is a matter of opinion. It's the main reason I haven't tried Kagi yet, and probably never will, as the owners don't seem to have a problem with any of it.
They want access to Yandex's index. Given the quality of Kagi's results, I trust them with that call. Despite the Ukraine war being of deep personal interest to me.
In the link above they say they added Yandex Image search as a provider.