This article seems to repeatedly blur the distinction between 'having space' to encode all the states inside a volume on it's surface and an actual theory of correspondence of states.

"Having space" is just a consequence of black holes. If you have more information in a volume than can be encoded on its surface in theory, you have enough mass inside the volume to make it a black hole and the event horizon then has enough space to encode the information even if the original surface did not.

The correspondence between information, thermodynamics, and mass that causes black holes to 'make it possible' to holographically encode all the information inside is what makes this theory so tempting. What if everything is information, and black holes aren't an expression of 'too much mass', but rather just a result of 'too much information to store'. This theory, if it existed, would demonstrate a key result of both relativity and quantum theory based on a very simple premise, and suggests it might then be possible to base both General Relativity and Quantum Theory on top of a simpler theory.

> That’s a violation of logic and geometry. It asks us to erase the categorical difference between square meters and cubic meters.

No, that's sheer nonsense.

> There is no negative mass, so you can always infer the one real arrangement of stuff inside from the warping of space-time at the surface of your box.

Positive mass does not make this argument work. Two bodies in GR can have different distributions of mass but identical exterior geometry. A counterexample is two spherically symmetric, uncharged bodies with the same total gravitational mass but different radial density profiles. By Birkhoff’s theorem, their exterior vacuum geometries are identical.