a city with a large Chinese population
Chinese in the above noun phrase is an adjective.
This adjective forms with others a series of cumulative adjectives, as shown below.
many cities with large ethnic Chinese populations
large ethnic Chinese in the above noun phrase are cumulative adjectives.
"Cumulative adjectives" are two or more adjectives that build on one another and together modify a noun. They're consecutive.
ThoughtCo
ethnic Chinese is more common than ethnically Chinese; hence, the following NP
many cities with large ethnic Chinese populations
is better than the other one you are also considering.
Ngram