Kagi -> Yandex -> Putin (through taxes), it's not really direct IMO
That being said Kagi -> Yandex hop does indeed make it indirect.
(I too have stopped using Kagi after I found out that they pay Yandex and employ people who support Russian war).
Yandex was split for a while into a Russian-controlled part and an independent part in the Netherlands, controlled by the original co-founder, which later become Nebius AI. Nowadays, these entities are completely detached, and Arkady Volozh has renounced his Russian citizenship.