What does “hawking radiation encoding the future through black holes” at all have to do with “humans intervening with and encoding their own signals over radio spectrums”?

Nothing.

Understood. Sorry. I should have given you the benefit of the doubt.

To me, the resolution of the paradox — that the radiated field might contain some encoded information in it — is less weird than the alternative, which is that the information somehow disappears. Information being encoded in a field seems natural to me. There’s a tight interplay between energy, temperature, and information. It’s even right there in the first law of thermodynamics: dE = TdS + dW. (The S is the missing information about the system.)