"given that destroying the correlation between two entangled particles" i think this is the assumption that is easy to make without digging deeper into entanglement.

i am still in the process of reading this article (https://arxiv.org/pdf/2408.06418) however entanglement witnesses can be realized in several ways and are one of the underlying aspects of how quantum networking can be made reliable.

under the category of heralded entanglement, one realization uses photons striking photo detectors after they meet in a beamsplitter under the hong-ou-mandel effect scenario. for type 1 entanglement with HOM: if the photons at the two input modes are identical, they always bunch due to quantum interference, and if the photons resulted from emissions in the respective quantum nodes those nodes are now entangled, and the detection is the classical signal that the entangled link was created. the nodes can now transmit information unidirectionally into the entangled qubits. for type 2 entanglement with HOM it's a little bit more complicated although the underlying concept of indistinguishability is what results in the entanglement just the same.

heres one experiment from oxford, https://www.nature.com/articles/s41586-024-08404-x, where they achieved this with high fidelity although the particular details of the beam splitter experiment are not as well detailed.

Although I am not an expert in quantum information, I think the problem you pose is resolved by the fact that the no-signalling theorem is about measurements of a quantum state, which is a microscopic state, and heat transfer is a measurement of a thermodynamic quantity, which is macroscopic. In much the same way that measuring the temperature of a classical gas doesn't give information on the location or momenta of the constituent particles, a thermodynamic probe of entanglement doesn't necessarily furnish precise information on how a state is entangled (e.g., Eq. 2 in https://arxiv.org/pdf/quant-ph/0406040).

Yeah the whole entangled system is present and interacting with the "thermal ancilla" in their setup.

Are you sure?