This will not happen because other countries are not going to pass on information to China of their new citizens. The Chinese citizenship is between China and the (now ex) Chinese citizen.
This is very wishy washy. "Not residing in China" does not mean they have citizenship elsewhere. They are unlikely to lose their ID number. What I could envision occurring is their hukou address being unregistered, forcing them to reregister when they are back in the country. Beyond that..
Unless other countries started sharing information of new citizens while also obtaining sufficient identifying information for another government to identify people nothing will happen and this is usual hand wringing.
No they don't. They are meant to declare it. Many do not. Most do not. Most are quite attached to China.
It is not tolerated. Again this goes back to Australia and other normal countries not sharing information of new citizens with foreign governments. If one was to travel to China on their valid Chinese passport after receiving Australian citizenship you travel as Chinese. If you travel on an Australian passport you travel as Australian. There is no way for China to tie these together (wait..) unless the person carries both and tries to use both. In other parts of the world one can travel on multiple passports and enter/leave countries on different passports. For example, if I had UK and Australian passport I could enter the US on my UK passport and leave on my Australian one and noone would care. However in Chinas case you need to enter and leave on the same passport as it contains your visa information (if Australian) and entry/exit stamps if Chinese. If you try to exit without entry stamps on your Chinese passport you will have issues and if you try to enter on your Australian passport without a visa you won't be able to. So you need to use the same passport for entry and exit purposes.
Thus if you have Chinese passport and an Australian passport you can enter and leave on the same passport you are treated as either an Australian citizen in china or as a Chinese citizen in China. There are various reasons to use a Chinese passport to enter China. You skip immigration (mostly) and it is faster to get out of the airport. You do not need to register wither either as hotel or the local police if you are staying with relatives. You are treated as Chinese rather than being treated as a foreigner.
And this is likely why there was drama around Wuhan flights at the start of the pandemic - Australia was trying to help "citizens" who had entered China on their Chinese passports and China was treating these people as Chinese, because in Chinas eyes.. they are.
In short the story that is being circulated sounds like bs.