From Bulugh al-Maram (Book 16, Hadith 1514) (sunnah.com):

Ibn ’Umar (RAA) narrated that the Messenger of Allah (ﷺ) said:

“He who imitates any people (in their actions) is considered to be one of them.” Related by Abu Dawud and Ibn Hibban graded it as Sahih.

As far as I'm aware, this is an authentic hadith, with Muslims applying it in their everyday lives as reason to avoid behaving like disbelievers.

Question: Does the above hadith apply to race in any meaningful way?

Or as I (semi-jokingly) phrase it in the title of the question: Does this mean I'm Chinese? [Obviously I'm being sarcastic, but not that sarcastic to be honest with you.]

Despite having no ancestral connections to China (that I'm aware of), I live in China and have become accustomed to a Chinese lifestyle. On occasion I say "I'm half Chinese", and once I was mistaken for a Uyghur Muslim.