They absolutely can implement China-level censorship right now, they have technical capabilities. In fact there have already been tests of complete isolation from foreign internet in remote regions of Russia.
They just don't use it much, yet. I guess they are afraid of consequences and prefer to let people live pretending that nothing has changed. He will go slow with it. Russia is still tightly integrated with western culture and economy (e.g. they have a strong IT industry and internet isolation will kill it for good). Russian culture has been aligning itself with European culture for centuries. They watch western movies and tv shows, read western books, half of the memes they use are from anglophone internet, etc. They are much closer culturally to Europe than to China, even despite all the politics.
Also legally the initial versions of this thing are from 2005, I think? Rather old. Just nobody cared.
2014 is when it started for real. At first the laws were rather innocuous (protect the children and stuff). But with each year they were "improved" to become more and more oppressive. Putin is smart enough to realize that if you do it incrementally then there will be less protests and he will appear as a good guy, "protecting the people". It was the same with "foreign agent" laws.