The Heisenberg Hamiltonian is $H_{Heis}=-\sum_{ij} J_{ij} \langle \vec{S}_i \cdot \vec{S}_j \rangle$ (generally, save different constants depending on convention). This seems to suggest that the exchange coupling parameters $J_{ij}$ would have units of energy/units of spin squared (i.e., $[\frac{\textrm{meV}}{\mu_B^2}]$). But every resource I've found reports $J_{ij}$ in units of energy, ignoring the spin.
I'm aware that, in atomic units, spin is written in units of $\hbar = 1$, but this only transforms the unit into an absorbable constant, meaning the unit is still there, just unreported. But even when venturing outside of atomic units, as many papers do in reporting exchange parameters in [meV], the units of spin are left out. Why is this? I've also seen some Hamiltonians written with unit vectors $\vec{e}_i$ replacing $\vec{S}_i$, as though seeking to preserve only the direction of the atomic magnetic moment without its magnitude. But this strays from the formalism.
What am I missing here?