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 the hell then in dS=Q/T the Q factor get's divided by T and not by some "abstract volume measure"? Why enrgy spreading is measured in units J/K and not in $J/m^3$ ?

Or, maybe, the temperature in dS=Q/T is treated exactly like some kind of volume.

I can certaintly think in this way:

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

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