It's hard to tell from the Quanta article, but without meaning to sound dismissive, a lot of this seemed like reexpressing some of the same ideas in different ways. The constructor and resource theories seemed very similar to me, for instance.

I was also extremely puzzled by the dismissal of probabilistic or statistical models as being fuzzy or something. Probability has always been the domain of possibility -- this is basically the Jaynesian-style account of probability. It's always seemed to me to be the case that at some level statistics is about selective loss of information -- that is, as you go from descriptions at the particle level to group-level statistical accounts, you summarize (in a coding sense) the ensemble of particles' behavior to shed information required to maintain complete information about the ensemble. To make an analogy, if you wanted to know people's heights, at some point storing information about 1 million person's heights would become burdensome, so you'd replace it with a single number (e.g., the mean) instead.

That's not to say what's being discussed in the article isn't interesting, but it just seems like a different level of analysis or something? There's also different ways of representing amount of information in the quantum realm vs classical realm, so there's that, but it's also the case that a chamber of gas will generally involve a lot of molecules in many classical cases.

I also had the sense that there was probably something more fundamental that you could invoke that would integrate a lot of this, at the level of logic or computational theory or something. But maybe at this level the difference is sort of moot.