> Broadcasts from international news sources that mentioned Peng Shuai were censored
I do not know about this specific issue. What I suspect is that now it has become a foreign relations issue, they are pushing for unity in messaging. Unity in messaging is a core principle in Chinese foreign relations practice.
> And what business does the CCP have, if Peng Shuai is free from the kind of imprisonment it is assumed she is under, telling the public when she will be making a public statement?
This is a matter of values. Westerners believe that government should interfere as little as possible in citizen matters. That's fine.
The Chinese don't tend to see the government in an adversarial manner. In general, they prefer a strong, centralized government that actively meddles in citizen matters as long as it is for the public benefit. They see the government as a partner (though, depending on times and context, "necessary evil" may sometimes be more appropriate) in building a better society rather than an enemy of a better society.
Furthermore, the CCP and the government aren't just a top-down imposition. They are the very fabric of society. They are everywhere. Every neighborhood has a neighborhood commitee who are party members. They help the neighborhood and perform important community management tasks. If you have a complaint about the neighborhood, you go to them. They regularly come ask you whether everything is fine, whether you need something. During Wuhan's COVID-19 lockdown they were the ones on the front lines, ensuring that health workers stay supplied and ensuring that food gets delivered to every household. The CCP has 90 million members, or about 5% of the population. Everybody has some relative that's a party member.
The Chinese public does not view the issue as "the govt is telling her to make a public statement". Rather, they view it as "the foreign public is making so much fuss about her, the government and the media are helping her voice get heard by foreign public". That her social media account remains blocked for now is seen as a completely separate matter, related to domestic social stability, which has got nothing to do with foreign relations.
Regarding the future of her censorship: that will be lifted once things have calmed down. See my case studies on Jack Ma and Fan Bingbing: https://news.ycombinator.com/item?id=29347811
With regards to the value judgement, it depends on whether you can accept that western values are not universal. I propose the thesis that they are not, because many other Asian and African countries have also criticized the western "our values are the only right ones" attitude.
Furthermore, the characterization of China being "totalitarian" is wrong because China is in no way comparable to the likes of North Korea or Saudi Arabia. You should check out the works of political science professor Daniel A. Bell: https://youtu.be/ckt94_JWHPs
This isn't a "coincidence". The Chinese government has evolved to its current form because of Chinese values. The CCP won the civil war because it had support of the majority of the population.
Han supremacism — while it exists — is largely not a thing and certainly not state policy. State policy is that minorities receive extra benefits that Han do not enjoy, and that the provincial government heads of minority provinces must be of those ethnicities.
Please go to China and tell a Chaoxianzu he's not Chinese. He'll tell you to fuck off.
Please go to China and tell people that the KMT should have won the civil war and see how people react.