Is Copenhagen or Many Worlds true? An experiment. What? Yes.

Skimming the paper I'm not at all impressed. In particular, they make frequent and incautious use of all sorts of approximations that are only valid up to a point under certain assumptions but make no attempt to bound the errors introduced or justify the assumptions.

This is particularly dangerous to do in the context of trying to demonstrate a failure of the 2nd law of thermodynamics as the very thought experiment that might be useful will generally break those heuristics and approximations. Worse, the 2nd law is only a statistical regularity not a true exceptionless regularity so what one actually needs to show.

Even worse this piece seems to be trying to use a suspicious mixture of quantum and classical notions, e.g., using classical notions to define a closed system then analyzing it as a quantum system

I don't think there would be anything as clearcut as a separation between objective and non-objective collapse. A more likely candidate experiment against objective collapse would be a quantum computer consisting of 10^2+ qubits.

we adopt in the following the hypothesis held by the majority of physicists, namely that the collapse process is real in the sense that it occurs independently from the presence of an observer or a measurement apparatus

Uh, no. Only a small minority of physicists think of the apparent collapse as an independent physical process. Most physicists follow the "shut up and calculate probabilities" approach, and most of those who venture into the nature of apparent collapse agree that it is very much observer-related, as in, the entanglement of the observer with the observed is essential for the Born rule to manifest.

Regardless, it seems like a good idea to target "the phenomena taking place in the little-explored realm where the quantum world interfaces classical physics", since this is where the mystery likely lies.

The different outcomes predicted for this experiment by quantum physics and by thermodynamics are distinguishable by measurements of the distribution of radiation in A and B.

That indeed seems doable, and both authors are condensed matter experts, one is a experimentalist, wonder why the paper does not hint at a potential experimental implementation.

I have my reservations about their interpretation of the proposed experiment, whatever the outcome, but I'd rather wait for the experts in the field to chime in. Someone like Scott Aaronson, for example.

Hmm, good thought.

One problem I see with the experimental setup is that it is impossible to remove the loss of energy from the system. For example, no mirrors are perfectly smooth, perfectly reflective, and perfectly aligned. Even if coherence is formed, it would still be at the cost of heat, so it would be unclear if entropy actually decreases.