Many books say that entropy measures energy dispersal or energy spreading. Spreading
Key point 1.4: Thermodynamic processes entail spatial redistributions of internal energies, namely, the spatial spreading of energy. Thermal equilibrium is reached when energy has spread maximally; i.e., energy is distributed equitably and entropy is maximized. Thus, entropy can be viewed as a spreading function, with its symbol S standing for spreading. Although not Clausius’ motivation for using S, this can serve as a mnemonic device. Energy spreading can entail energy exchanges among molecules, electromagnetic radiation, neutrinos, and the like.
Spreading where? Spreading in space? What kind of 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).