Not that it answers your question, but the move happened in 2020 to "hire more easily, act more swiftly, and pursue ideas that were previously not possible".
Just in case you need sources: Kagi is using [1] Yandex and paying them as of June 2025. This is a long-standing position, which was also voiced [2] in November 2024.
Regarding Yandex. The founder sold [3] the assets (seemingly including the index and Yandex trademark) to VK (Mail.ru) in 2022. VK are known supporters of the war [4]. The founder subsequently renamed [5] his original company to Nebius Group and pivoted towards compute for AI.
I've collected some links here last time this was discussed: https://news.ycombinator.com/item?id=46057759