This is a naive reading of what has happened.

There may well be some cross immunity in some communities due to previous coronavirus circulations. And the numbers in China are not all that credible - one guy at my work had three of four grandparents die of "some winter cold" in March last year. It will be quite some time before the numbers in China become clear I think.

I think if China didn't manage coronavirus successfully we'd have seen numbers of deaths due to "some winter cold" so large that even communist party wouldn't be able to hide

Really? They did a pretty good job of hiding a host of vast reeducation centres....

Did they? You can rely on your reader to know that you're referring to Xinjiang.

At this point - but these centres were revealed to the world (by journalists who are now kicked from the country) fully built and also full of inmates.