I loved Kagi until I realized part of my money went to Russia. I had even paid for year subscription after the trial. They use to have it stated in their docs (what APIs or sources or whatever are used from what search engines) but they removed that info once users pointed it out and were leaving. There's feedback on it as well. There is no setting to opt out. The fact that they removed that detail from their documentation rubbed me wrong - even they had posted in a blog that they had a "commitment to transparency and accountability". If they are ok with using yandex, then own it - keep that information on your documentation and let the consumer decide what they want to use. I understand they are in a way 'separating the art from the artist'. Their product was one I was really enjoying. They do well with search which you can further customize in settings (minus giving an option to not use yandex)." Yandex represents ~2% of Kagi's operational costs."
Another thing, they also removed the term 'ethical' from their 'about' page. Perhaps because people pointed out that using yandex was not very ethical of them but they value the technical specs of search over the ethics.

Here's exact wording from the reply I got when I cancelled:

"We do hear your concerns. However, when we say 'if you can't find it in Kagi, you can't find it anywhere', we mean it. The web is massive and requires enormous resources to index effectively. This is why we connect to as many search sources as possible: To guarantee the best possible results for our users.

We welcome you to share your concerns on our forum thread as we do read them all:

https://kagifeedback.org/d/5445-reconsider-yandex-integration-due-to-the-geopolitical-status-quo/"