Yes, governments targeting 'false claims' is always a bad idea, as we have ample evidence for in the West. Still, it's a better fig-leaf than "people say stuff we don't like", so they use it anyway.

Yes, it does send a 'chilling message'. But you can't go around claiming that "in Russia" you go to jail for calling what Imp calls "the women's war" a war. Not without citing even a single instance.