Yes, bad things do happen in China. There is racism. The government lies and covers things up. They allowed the virus to spread until they could no longer ignore it. All of those things are also true of the US. We also know that the virus started in China. None of that means that you are justified in calling COVID-19 the "Chinese virus". To do so only has one purpose--to vilify people who are Chinese. It leads to the same kind of behavior in the US that we now see against Africans in China.
I disagree on them letting it spread. They cracked down hard once they understood what they were dealing with.
It's fair to say that they did crack down hard for a while after local officials tried to cover up the outbreak, but lately they seem to have gone back to the practice of trying to minimize the magnitude of the problem by manipulating their statistics and spreading misinformation--e.g. trying to shift the blame onto the US government. For example, they don't count reinfections, once people are declared to have recovered. It isn't realistic to think that all of their cases are now being caused by people entering China from foreign countries. I think that much of this is a reaction to Trump's demonization of China, but the Chinese government is run by people who think that it is more important to control the narrative than to let the chips fall where they may. I suspect that their recent behavior is more of a reaction to Donald Trump's behavior towards them, but they have been extremely embarrassed by the fact that this crisis started in China. Trump has used China as a scapegoat for his own incompetent response to the crisis, so, IMO, China is trying to punch back. Russia is also scapegoating the US in an effort to deflect blame for their own unpreparedness to deal with this epidemic. Worse than the COVID epidemic is the epidemic of finger-pointing by governments and leaders in their efforts to avoid blame.
I do agree the local officials did try to cover it up--but that's part of not yet knowing what they were facing. I don't see them spreading deliberate misinformation--the death toll is certainly higher than they are saying but they don't know the true numbers, either--plenty of people died without ever being diagnosed. Fog of war, not misinformation.
As for reinfections--why would they count as new cases?? Especially since they probably are just a false negative on people who are no longer symptomatic but don't have 100% clearance. (And note that you can get a positive off viral material that isn't actually infectious--it's not looking at the whole genome.)
I think they have had a local outbreak that they stomped on again, but why do you think it's not people entering the country? Everyone gets quarantined and tested.
I do agree China is trying to punch back on a PR level, but I don't see that meaning they are lying about the numbers.