Can somebody point me towards the entrance to whatever rabbit hole explains why thermal information is not information? I must be missing something.

You can set up a torsion balance and extract a bitstream from the way it dances in a warm gas, and each of those bits fits, albeit with some creativity, into Shannon's definition of information: Once the balance jiggles in a 1-like way, you can exclude the universes where it would've jiggled in a 0-like way from your list, thus reducing the set of candidate universes by half: one bit.

Maybe we can't reconstruct the words on the book that fell into the hole without an impossible-to-achieve perspective, but that doesn't mean it's not the same amount of information. Does it?