What came up in comments to this answer to the question quoted in the OP, is that one has to distinguish, one the one hand, phenomenological vs. microscopic models/theories and on the other hand, macroscopic vs. microscopic scales/quantities. The meaning of word microscopic and what it is opposite to depends on the context (alas, human language is ambiguous - but we all know that, although carrying a suitcase up and down the staircase results in zero work, it does cost energy and makes one tired.)
As far as the models are concerned:
A phenomenological model is a scientific model that describes the empirical relationship of phenomena to each other, in a way which is consistent with fundamental theory, but is not directly derived from theory. In other words, a phenomenological model is not derived from first principles. A phenomenological model forgoes any attempt to explain why the variables interact the way they do, and simply attempts to describe the relationship, with the assumption that the relationship extends past the measured values.
One the other hand, when talking about scales:
When applied to physical phenomena and bodies, the macroscopic scale describes things as a person can directly perceive them, without the aid of magnifying devices. This is in contrast to observations (microscopy) or theories (microphysics, statistical physics) of objects of geometric lengths smaller than perhaps some hundreds of micrometers.
Internal energy is a quantity that exists both in (phenomenological) thermodynamics, and (microscopic) statistical physics. This is a quantity describing a system with a huge number of particles, $N\sim 10^{23}$, and directly measurable - this is why, in terms of scale, it is a macroscopic quantity.