For the China part: Yes, the "by force" part certainly exists as a position, in competition to the peaceful unification approach. It's important to keep in mind, though, that the confrontative position of the first Trump administration and afterwards the Biden administration significantly helped the "by force" faction. There was an interesting piece in Foreign Policy about that, a social scientist from the US was questioning Chinese students at an elite university on this very topic and thus had the chance to do a time series observing the attitude change following US actions.

Secondly, in Taiwanese politics, Unification is actually a big topic and even has its own party, the New Party, advocating for it (plus the fringe CUPP). Not popular right now, but certainly existing - and evidently falsifying the notion that the all of "Taiwan doesn't want to be part of Beijing's China".