None of that accomplishes anything if they don't put that part of their identity up front and center. The general public has no idea he's Filipino, as with 99% of the other Filipinos in American entertainment.
There are plenty of Blasians in the Black community. My Mom is one, one of my best friends is half Black, half Filipino. They would acknowledge their ancestry but they would still consider themselves Black because that's how everybody else views them and how America has labeled them for centuries. My Japanese grandmother was disowned by her Japanese parents for marrying a Black man. It's just hilarious to me how this is relatively a new phenomenon of other groups claiming them once they become big despite the prevalence of Anti Blackness sentiment in non Black cultures.
What's the point of heritage if their heritage only reflects the Black part?
How does Bruno Mars infuse pinoy heritage in his music or dances? Why is he backed by all Black members?
I don't like this pretense that you're forced to incorporate elements of all your cultures in your music though. A lot of Asian Americans that are children of first generation immigrants already become Americanized. So they either occupy or take interests in what is dominant in American culture: which in music today, in my opinion, is heavily dominant by Black artists. Beyoncé, Rihanna, Drake, Kendrick, The Weeknd. Just because you're a certain ethnic group does not mean you should be confining yourself to only listening or portraying aspects of your culture when you live in America. Just because you're Japanese doesn't mean you should only listen to Japanese artists, it doesn't make you any lesser if you enjoy American media. And just because you're biracial, it doesn't erase all of you just because a certain part of your descent is more visible than the other.
He faced backlash from the music industry because he was Asian, a lot of execs wouldn't back him because of that fact. It's just rather unfortunate that you have to constantly remind people that you're Southeast/Southern Asian in America when you don't fit the general mold of what "Asians are supposed to look like." You have to constantly remind people "hey, I'm FILIPINO, I'm INDIAN, I'm THAI" in everything you do or you're not "Asian enough," whatever that means. You literally have a group out there named Far East Movement and people were trying to serve dazed and confused when they found out they're Asian because their hit song, Like A G6, borrowed from Black culture.
Regardless, how do you suggest he puts his culture in full display musically? In Filipino entertainment, it's heavily Americanized. A lot of the variety shows and larger interest in music are primarily dominanted by American artists. Sure, Filipino musicians co-exist with them on the charts, but they're mostly driven by Filipino rock or Filipino ballads or hey, Filipino rap, which heavily borrow from American culture itself.
And to address your anti-Blackness point:
I don't speak for all cultures here. But I feel anti-Blackness is moreso about skin tone rather than race in a non diverse country. American exportations drive a lot of perceptions about Black people abroad but there were already negative connotations with darker skintones in those nations prior to imperialism so that already muddies and worsens the situation a bit.