your [0] is just silly. If a person is at risk from their state's law enforcement, handing over their search data to yandex just makes it easier for Russia to convert them into spying/sabotage activities through, e.g., extortion.
As you have noted, Russia is at war with the ~English-speaking world~ West, so it is much more likely to use this data against the users than in the past.
But in your example the person involved would rather cooperate with the Russian authorities than turn their data over to local law enforcement. So it clearly makes sense to this hypothetical individual.
Besides, it'd be a struggle for the Russians to even figure out who they are. They'd only have search data. That is powerful but probably not enough in many cases.
As you have noted, Russia is at war with the ~English-speaking world~ West, so it is much more likely to use this data against the users than in the past.