...It’s not obvious that “middle class” as a concept is a cultural universal, much less that middle class norms are the same across cultures.
The concept of "middle class" (in the "middle class norms" sense) is increasingly co-evolving with existing cultures in a way that makes it more of a cultural universal. And cultures which don't adopt the middle class concept tend to fail at basic human flourishing, which is as close to a universal as it gets. Marx was well aware of this BTW; he thought socialism would be infeasible unless and until the "middle class norms"-based stage of history (originating from early-modern-age Europe at the latest, not the 20th-century Anglosphere) had fully played out in most of the world, at which point it would be superseded in a quite natural way. See also Scott's post "How the West was won", which is relevant to this question.
I agree that if you assume there's a natural direction of cultural progress, a set of stages all cultures have to pass through (or leapfrog by assimilating into a more advanced culture), then the "middle class" could be a cultural universal in the sense of being an essential attribute of one of those stages. But it's not at all obvious to me that Marx was right. Even if he was, it's not obvious that the actually existing acculturation people do to participate in the global cultural middle class is entirely composed of culturally universal middle-class traits, rather than accidental traits attributable to the particular areas where this culture emerged first.