So far they've had to have ugly lockdowns in a few cities, but it's a tiny fraction of the overall population.
If it goes on for a long while - this will be a problem, but if they got away with it by having lockdowns - even late into the game - I wouldn't call it a failure.
That said, we really don't know what a lot of the numbers are.
I am sure similar data exists for US states, EU countries, etc.
Yes, people believe in mask mandates because masks are an effective way to prevent the spread of COVID. This is indisputable, so of course people support mask mandates.
> will have eased up the censorship reflex present in some Western media/social platforms
You can say whatever you want about COVID on social media in the west -- worst case your post is displayed with a warning stating it may be misinformation (and there is a lot of misinformation on western social media).
Probably it will take at least one year and a half - two years, at least that's how long it took the Western authorities to somehow change their discourse. Some people around the Western parts of the world still believe in mask mandates, to say nothing of the vaccine mandates if you want to visit their country (Greece, for example).
Thankfully all this China situation will have eased up the censorship reflex present in some Western media/social platforms, now it's again cool and super ok to complain about the lockdowns and to call them authoritarian because it's the evil Chinese that are implementing them. When us, the West, were doing them it was "for democracy" and for the greater good (for "the demos"). When the streets of NYC or London were empty because of lockdowns it was a civic thing, when the streets of Shanghai are empty (as The Economist was decrying in one of the its latest issues) is because the Chinese authorities want the worst for their people.