I have a similar background with you, only that my focus is Japan - I did my master’s in Japan and I’m not Japanese (US citizen with another nationality, but I hardly call myself American and English is not my native language either), I also got 2 rejections, 1 MA, and 1 Ph.D offer with funding (I guess I’m just lucky)
I do feel like US grad schools prefer students with an MA from an English-speaking country, as the POI of the school that gave me the MA offer told me so. But at the same time, for some schools having international experiences is also a plus, so don’t give up!