"forward" means "progress" which means "left". I don't really see the point there :P I've seen many parties claim "we are not left-wing or right-wing" but they evidently have to be either.
In the case of "Macron", forward was clearly "right", as it was mostly about getting rid or reducing social schemes. In France, "neither right nor left" generally means "right".
If what you say is true, there must be some underlying outlook or philosophy that leads to one or the other.
What I suspect is that's true for some kinds of issues, but other issues are more of a mixed bag that just happened to end up polarized. Maybe those other issues are important enough to make a third party worthwhile.
forward in Yang's case means "anti incumbency". Not sure if that's leftist or not because incumbency is basically a mainstay of the current political system of both parties.