In the case of African American, Africa is a continent, so is it indeed understood to mean an American of African descent and who most probably doesn't have citizenship in any African country? Same with Asian American?
There's kind of a problem I notice with cases where we're dealing with non-continents say
2.1 - Filipino Americans: For example, Wesley So (world champion in chess 960) was a Filipino citizen and then now is an American citizen but not a Filipino citizen. How do you distinguish Wesley So from other people who are actually dual citizens of both the US and the Philippines? And btw, is it indeed correct to call Wesley So a Filipino American as opposed to a Filipino-born American?
2.2 - Cf Alireza Firouzja, another chess supergrandmaster, is indeed a dual citizen of both France and Iran, so we call the guy Iranian-French. Would we actually use the term 'Iranian-French' to describe citizens of France who have Iranian descent?
2.3 - Chinese Filipinos: I think this was what Wesley So was up to 2013: a citizen of the Philippines who has Chinese descent but didn't have any citizenship in China. How would you have distinguished Wesley So from people like me who are actually citizens of both Hong Kong and the Philippines? (Btw, I don't necessarily have any Chinese descent, but my paternal relatives and I are said to look a little 'Chinese'. Also if Hong Kong vs Mainland vs Macau is an issue, then just pretend I'm a mainland citizen instead of a Hong Kong citizen. Afaik, Hong Kong citizen just means Mainland citizen with Hong Kong residence or something.)
Strictly speaking, are the terms African American, Asian American, Filipino American, Filipino Chinese, etc actually wrong? Eh, I just wish people would say like Y of X descent instead of X-Y if that's what they really mean of course...and assuming it's correct lol. Cf Raven-Symoné says 'I’m not an African-American. I’m an American.'
The term "African American" has a meaning that's based on decendancy rather than any notion of dual citizenship. See this overview on Wikipedia. The meaning of the term "African American" has a unique socio-political context that doesn't generalize to the other combination descriptors, but none of the terms you've listed imply anything about citizenship.
Strictly speaking, are the terms African American, Asian American, Filipino American, Filipino Chinese, etc actually wrong?
No. Strictly speaking, these terms do not have the meaning you're assuming about them. They imply only descendancy or community, not citizenship.
I just wish people would say like Y of X descent instead of X-Y.
When it is important to distinguish between citizenship descriptors and descendancy descriptors, it might be helpful to use more specific phrasing as you suggest, but it would be important to explain what you mean so that people don't assume the more general meanings.
Raven-Symoné says 'I’m not an African-American. I’m an American.'
Self-identity is complex and I would defer to anyone's own description of their identity.