"Homeless" has a kind of stigma to it (maybe you picture a dirty bum on the street), while "unhoused" doesn't because it's so new. It simply sounds like a category of analysis devoid of emotional judgment. (Like maybe they're unhoused because a hurricane just blew down their house, not because they don't have a job.)
If "unhoused" comes to replace "homeless", I'm sure we'll get another term to replace it, once "unhoused" has acquired the same stigma that "homeless" does now.
Though I've got to say that "unhoused" is a particularly uncreative term! Essentially a literal synonym of "homeless". It's like they didn't try at all this time...