Do Chinese cellular companies offer eSIM service for iPhone 16 pro purchased in the USA?

No, In China mainland no carriers support eSims.

The Chinese government prohibits the use of eSims there.

In Hong Kong, some carriers offer the option.

click here ➜. Find wireless carriers and worldwide service providers that offer eSIM service - Apple Support

I’ve seen reports that not all do. You’ll have to research the particular carrier you are interested in.