Yandex isn't on any sanctions list as far as I know, so Kagi is free to do business with Yandex. Yandex did need to reorganize (as their Dutch tax avoidance parent company was obviously causing them issues) but looking at https://ir.yandex/press-releases?year=2024&id=05-02-2024 it seems like all of Yandex has been sold to a generic Russian investment fund.
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.
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.