No or they wouldn't be hit.
"The will" is so sparsely enforced there could be none, and, for example, Putin directly oversees a very, very small amount of topics. One of which is, for example, hypersonics program.
The rest is controlled by a whole goddamn lot of influence groups which president administration mediates (do not confuse with duma and federation council, those are mostly talking heads). For example, current internet censorship breakdown has nothing to do with actually censorship but with a small group of influential people who seek monetary interest in diverting traffic to their wannabe clones of western media.
No, I don't know why they chose such structure nor I have any idea why they selectively enforce one topic and completely abandon another.
Yandex is one of the most disloyal and pro-ukraine companies in Russia, it to this day does not recognize Crimea as Russia yada yada. It's own AI systems are hardwired to refuse any pro-russian topics and only cover pro-ukrainian side. In that way, gemini and chatgpt are both significantly more pro-russian, which is hilarious (if only they didn't block RU region).
Being state owned means nothing if there are no will to trample down disloyalty.
Again, see core comment. People in this thread cheering for yandex bombing really don't understand a single thing.
Listening to russians they are, in fact, the force of good in the World, not a colonial power profiteering from extinguishing hundreds of peoples across Asia and occupying half of Europe for good part of 20st century, not at all.
What next? Bolshoi theater and tolstoyevsky?