However, there is another paper that proposes that gravitational time dilation can result in decoherence in composite quantum objects.
This calculation is done with standard quantum theory, so is more robust.
Universal decoherence due to gravitational time dilation

The physics of lowenergy quantum systems is usually studied without explicit consideration of the background spacetime.
Phenomena inherent to quantum theory on curved spacetime, such as Hawking radiation, are typically assumed to be only relevant at extreme physical conditions: at high energies and in strong gravitational fields. Here we consider lowenergy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to decoherence of quantum superpositions. Time dilation induces a universal coupling between internal degrees of freedom and the centreofmass of a composite particle. The resulting correlations cause decoherence of the particle's position, even without any external environment. We also show that the weak time dilation on Earth is already sufficient to decohere micron scale objects. Gravity therefore can account for the emergence of classicality and the effect can in principle be tested in future matter wave experiments.
https://arxiv.org/abs/1311.1095


The idea is that coherence in composite systems requires that the subsystems evolve identically, so they always remain in phase. Decoherence then corresponds to processes that disrupt the evolution of the individual parts of a composite system. In the case of gravitational time dilation, the evolution of the constituent parts then depends on the gravitational potential. Given that we can now detect changes in the gravitational potential on the centimetre scale using our most precise clocks, this effect may not be negligible on the microscopic scale. Maintaining a quantum superposition requires coherence in the system. Therefore, gravitational time dilation provides yet another factor in the decoherence of superpositions (there are many more factors that come into play as systems become larger, adding more degrees of freedom).
Overall, this is an active area of research. If you are interested in knowing more, then the following review article may be of interest:
https://iopscience.iop.org/article/10.1088/13616382/aa864f