then does that mean if a foreigner, say a pregnant woman from Finland, moves to China and has her child, and that child grows up in China, speaks, reads, and writes Chinese as their first language, has only ever lived in China... does that make them "Chinese?"

It just occurs to me that in terms of more old examples (not modern immigration stuff), there are actually quite a few "Chinese" historical figures who are genetically from a foreign place. The most famous example is, obviously, the two minority ruled dynasties, Yuan and Qing, where invading powers sinonized after invasion, adopted 中文 and the writing system 漢字 into the official documents. They are, culturally, considered "Chinese" (again, from an anachronistic perspective after the concept of the nation-state). Kublai Khan, for example, is considered Chinese culturally, because he has a Chinese name (忽必烈) and a Chinese "regnal title" (憲天述道仁文義武大光孝皇帝). Even though most Westerners would consider him to be "Mongolian" due to being the son of Genghis Khan. But in China, culturally, Genghis Khan is considered a foreigner while Kublai Khan is considered Chinese.