My wife and kids were born in Japan, and I lived there for several years. Osaka is a huge star there and I can assure you, that if your mother is Japanese (and you were raised by her), you are almost certainly Japanese yourself, culturally speaking! Yes, there is a progressive movement in Japan to embrace multiracial citizens as fully Japanese, which Osaka's role in the ceremony represents (and Hachimura as the flag-bearer), though some old-timers are not completely on board with that idea and the term "hāfu" is used informally quite often. Ironically, because Japanese tend to think of their nationality in racial/genetic terms, the fact that she lived outside the country for a long period of time is not as significant as it might be for people in other countries.
The citizenship issue is more complex than it seems, however. The Japanese government requires that a citizen holding a second citizenship must declare at age 22 if they wish to remain Japanese citizens or renounce it. On the surface, choosing to be a Japanese citizen would seem to have the appearance of relinquishing one's American citizenship; but that is not strictly true because the American government does not accept such a statement to a foreign government as proof that you really wanted to give up your citizenship. Thus, if Osaka wanted to, she could claim Japanese citizenship at age 22, telling them she had given up her American citizenship, while still retaining her American passport as well as all other rights and duties as an American. In fact, it turns out to be surprisingly expensive and difficult to renounce American citizenship because they want such citizens to continue paying taxes on their worldwide income. The question of whether a dual-national Japanese citizen would actually relinquish their citizenship will ultimately depend on their tax situation. In Naomi's case, I guess it would be advantageous for her to truly relinquish American citizenship and the taxes that go along with it, but for others in different tax situations, it might make more sense to relinquish Japanese citizenship, or just hold on to both. It all depends.