> Chuck a steam engine behind the event horizon. We can’t know anything about it apart from its mass, but I claim it can still do as much work as before.

He has only half the "no drama" conjecture here. Given a sufficiently massive Schwarzschild BH the steam engine would work for a while before the Weyl curvature spaghettifies it.

As he says a few paragraphs above, the BH area increases when the engine enters the BH. To leading order the increase is driven by the stress-energy of the steam engine, and the stress-energy tensor encodes terms such as chemical and electrostatic potential energy, enthalpy, free energy, internal energy, virial stress, and so forth -- not just mass, although mass tends to dominate in simple systems. At early times the steam engine's entire stress-energy is outside the BH; at later times, the residual stress-energy of the steam engine (having lost some to radiation flying to infinity doing work earlier) is entirely within the horizon. I don't see why he objects to this "saving" of the second law.

Also,

> It’s all about forgetting information.

Well, it's thermodynamics that reveals the forgetting of information because of the classical irreversibility of crossing the horizon (classical BH never shrinks).

[Quantum vacuum causes classical black holes to shrink, but the Hawking radiation does not come from inside the black hole; it comes from defining a quantum vacuum as a no-particle state at an early time whereas the (Lorentzian) no-particle condition depends on the metric, and the metric for a collapsing-then-evaporating black hole is time-dependent (M is not eternally the same). By the equivalence principle, we can relate the disagreement between observers about the particle count in a state. In flat spacetime, A's no-particle state may be full of particles for observer B who is accelerated relative to A (this is the Unruh effect); in curved spacetime B who is a region with an event horizon is accelerated relative to A and C who are in regions without an event horizon. Inertial/Eulerian observers A and C may agree that each's "no-particle" vacuum state has no particles; B will see particles in A's "no-particle" vacuum and in C's "no-particle" vacuum.

> The system is really the entire space-time

Here the author is entirely correct.

In the paragraph about no-particle state, the entire spacetime has a region with some nonzero stress-energy localized as a collapsing dust and otherwise everywhere the expectation-value of the stress-energy -- <T> rather than T -- is zero and there are no-particles outside the outermost dust particles. There is another region where there is an event horizon and no dust particles outside it. But there are particles outside and near the horizon, but everywhere far from the horizon <T>=0 and we find no particles there. There is another region where there is no horizon, and an expanding cloud thermal particles with the spectrum of a blackbody radiator that started cold and got extremely hot, but with none of the initial dust particles from the first region, and beyond that a no-particle region.

The broad research programme in numerical relativity is to trace the stress-energy tensor (and its generators) through these regions. Unruh discusses this in the context of a sonic analogue of a black hole: https://pos.sissa.it/043/039/pdf