I’m a first generation immigrant who immigrated to Canada at a young age and still retain my Chinese ability. The identity struggle is real. But it depends on the person.
Most of my CBC/ABC friends would identify as Canadian/American first and foremost and as do I. How long you spent in China before you immigrated abroad makes a big difference too. Most of my Chinese friends who immigrated high school age or later identify more with China than with Canada.
I’m more of a special exception because even though I think of myself Canadian my personality traits still trended Asian. So I travel Asia often and found South Korea to be the place that fits me the best. After traveling mainland China I just couldn’t accept the culture differences, part of the reason being that Chinese tend to be more anti-West than Koreans are.
My brother was born in Canada and is fully Canadian, gets along well with Canadians and fits well in Canada which is good for him.
So for everyone is different. I think the place you grow up in tends to be the place you identify with for most people.