Entropy is certainly a physical “thing”, in the sense that it affects the development of the system. You can equally well apply your argument that it isn’t a physical thing because it doesn’t exist on a microscopic scale to temperature. Temperature doesn’t exist when you zoom in on single particles either.
There’s no reason to involve our knowledge of the system. Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
> Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
That number also exists independently of the system! I can imagine any system and calculate the corresponding number.
(And for an even more philosophical question, does the “system” really exist independently of us? What separates the “system” from anything else? Is every subset of the universe a “system”?)
Exactly! Temperature isn't fundamental. It's a statistical measure made up by humans. It's certainly a very useful abstraction but it isn't a fundamental property. It describes an emergent pattern observed in larger systems. Same for entropy (and also AFAIK angular momentum).
It's entirely possible I'm wrong about any of the above but if so I've yet to encounter a convincing line of reasoning.