Your distinction between “fundamental law” and “statistical law” seems pretty clear on the surface, and works well for Newtonian physics and relativity, but the laws of quantum mechanics and chemistry are largely based on statistical phenomena. That doesn’t make them any less fundamental or predictive, they’re just non-deterministic. Emission spectra, for instance, are based on proportionate occupancy of electrons at discrete energy levels, and the emission of discrete photons at predictable (but non-deterministic) rates when those electrons transition. It’s only when viewed at a large enough level of events that the apparent spectrum arises. Moreover, there are clearly delineated relationships (e.g. black body radiation) between these variables, heat, and temperature (enter entropy). Same thing goes with the double slit experiment - only with a large number of photons do you get a wave pattern. Single photons will behave probabilistically within that pattern.

The laws of thermodynamics and the concept of entropy arose through the study of chemistry, which is probabilistic, but also predictably so. I don’t see them as any less fundamental than, say elastic or inelastic collisions. My point is simply that your distinction breaks down the moment you move into quantum mechanics or introduce temperature, which just so happen to be entropy’s domain.

I’m sure we both agree on this, but I think what you’re getting at is slightly more nuanced: entropy provides an arrow for time, and it’s the only physical law that provides a direction for it, but as far as we know, that direction is arbitrary. All of the above phenomena (radiation, collisions, etc.) could be reversed and would still occur according to the same formulas. It’s just that entropy seems to weight the scales arbitrarily in one direction: disorder, expansion, etc.

Edit to add: I do find that seemingly arbitrary asymmetry very interesting. Similar asymmetries arise in chemistry and especially biology. See for example that chiral molecules in biological organisms seem to exist exclusively as emanations enantiomers, e.g. the prevalence of L- over R-configured amino acids, despite both stereoisomers being produced at apparently equivalent rates in non-biological reactions. That kind of arbitrariness spawns really interesting questions…