I don't think there's any way it ever could. On top of what has already been mentioned, vis a vis "there is no one Asian culture, and several of the Asian cultures are doing just fine in the movie space, thank you", there's also. . . Black Panther is, at its deepest narrative DNA, about "black-ness". Its not just a character and story and mythos about black people, starring black people. Its "spirit" was about all these social topics, from the very moment Wakanda was created as "an African kingdom never colonized". A movie adaptation could work well or poorly, but it couldn't help but be about cultural issues of race and colonialism and etc.
Shang-Chi? Does not have that. Its creative premise is no more "about" Asian cultural issues than any other story involving kung fu. Such could, in theory, be added in an adaptation, but it wouldn't be as integral and natural. Thus I cannot see it having the same impact, because its not just what you are about, but how you are about it. Shang-Chi might well be important in providing a lot of jobs for Asian-American actors in Hollywood, but that is not going to be the basis of some vast cultural movement.