They do though, some of personal blogs i follow also banned in China; There is a saying in my circle of friends in Mainland China that the blog is “certified by Great Firewall of China” if a person’s blog got blocked

They also monitor internet communications and you can get your account deleted or a police visit if you post something to critical of the state. That's probably irresistibly attractive to Putin.

In my time working at a hosting provider we would get these very strange requests from the Russian government demanding Russian websites customers had with us be taken down for moral violations. Like a DMCA but for free speech.