I stumbled on the thread dealing with 5-year visas (or residence permits), which led me to this link.
https://www.scmp.com/news/china/soci...ou-qualify-new
One quotation from the link was: " According to China’s official definition, a foreigner of Chinese origin refers to a former Chinese citizen who has obtained foreign citizenship, or the
offspring of present or former Chinese citizens."
My deceased wife was born in Wuhan and was a Chinese citizen for her whole life. I am an American citizen, By her I have a 17-year-old boy and a 13-year-old girl who were both born in the US. In stumbling on several articles, it appears that when my children turn 18, they have the right to apply for Chinese citizenship. I realize that China doesn't permit dual citizenship, and I they certainly wouldn't consider encouraging them to become Chinese citizens now, but if they do have the right to become Chinese citizens, it could give them interesting choices 20 years from now. (assuming that Chinese citizenship doesn't have to be claimed a short time after your 18th birthday.)
An interesting side light to this is that I and my children have the right to become dual citizens of Italy by virtue of my Italian grandfather.