Many books say that entropy measures energy dispersal or energy spreading. Spreading where? Spreading in space?

I mean, that in my mind "the spread of energy" is some kind of "density of energy in some volume". Why then in $\mathrm dS=Q/T$ the $Q$ factor gets divided by $T$ and not by some "abstract volume measure"? Why is energy spreading measured in units $\mathrm{J/K}$ and not in $\mathrm{J/m^3}$ ?

Or, maybe, the temperature in $\mathrm S=Q/T$ is treated exactly like some kind of volume.

I can certainly think in this way:

The greater the $T$, the greater the number of "microstates" consistent with that $T$.

P.S. I'm aware about Boltzmann definition of entropy. I understand it. I just can't handle entropy in phenomenological level (classical thermo level).