When you go deeper into physics, mass and energy don't seem real either, in that, like entropy, they're emergent properties of a system rather than fixed, localized things.

I always thought of the energy of a system (kinetic + potential) as a useful mathematical invariant that helps us predict systems rather than a physical thing. If you put a cart at the top of a hill, then the cart has more potential energy (but only from certain reference frames). It doesn't feel like that potential energy is physical. It doesn't have a specific location; it's a property of the whole Earth-cart system. And yet, it's this total energy that gives rise to the physical properties we're familiar with. In fact, almost all of the mass in your body comes not from the mass of elementary particles, but from the potential energy in the bonds between quarks. Your mass is more than 99% from potential energy.

And then when you get into Quantum Field Theory, it turns out particles (like electrons) are no longer truly point particles but rather another emergent phenomenon from ripples in an underlying field. A particle is just a model that describes it well when looked at from a distance. (I hope I'm not butchering that, as I'm not a physicist.)

So mass, matter, energy, and entropy are all emergent properties of a system rather than being localized, "real" things in the way we'd intuitively think. And at that point, I'm not sure how we would define "real" or why it would be a useful distinction. Is there a useful insight to be gained by putting entropy in a different category of realness than mass?