Yeah, it is different, but once you know what you're after you can measure. It's a "type error" to ask for the number of bits of entropy in a baseball, but if you ask for the bits of entropy of a baseball given everything you know about the baseball (i.e. mass, composition, temperature), then you can measure it. You could even design a special instrument which makes relevant measurements of observable quantities and then calculates the entropy of a given object from those.

Temperature is actually defined from entropy, it's the change in energy per change in entropy. So it too is inherently subjective. One way to think about this is that to a simulator or god outside of our universe, who can precisely see everything happening in the universe, the temperature and entropy of everything is exactly zero (of course, they would be able to predict what we would measure it as). To them, they would see the level of a thermometer as simply a mechanical consequence of all the particles nudging it to that exact place (like you would if you saw someone pump the mercury up the tube -- you wouldn't conclude it must have gotten much hotter suddenly).

> So far as I know, entropy is pretty unique in that there isn't, and will never be an instrument that gives the number of bits in a baseball.

Nonsense. Black Hole entropy is measurable in exactly the same way - put it on a scale, get mass in kilograms, from mass compute radius and area - voila, you've got an entropy