The local theory part of the Carney et al paper (preprint <https://arxiv.org/abs/2502.17575>) is interesting in that it isn't obviously related to string theory / holographic entropic gravity. Instead masses induce a spin polarization near them which is a lower entropy state. Two masses with two polarized spin-clouds will attract each other as the system tries to thermalize to a higher-entropy state. With careful choices of parameters, they can generate any central force, and they explore a particular choice which corresponds to Newtons 1/r^2 mutual attraction.

The paper cannot deal with fast-moving masses at all: it's not just the relativstic regime (where speeds are significant fractions of c) but rather the masses must move more slowly than the thermalization. This is hugely restrictive.

Finally, comparing themselves to the traditional approach of quantizing perturbations (e.g. turning classical (General Relativity) gravitational waves into lots of spin-2 gravitons) the authors write:

  The gravitational interactions we observe at accessible
  length scales could in principle emerge in many ways from
  physics at the Planck scale ρ ∼ mPl/ℓ3 Pl ∼ 10104 J/cm3.
  Perhaps the simplest is that gravitational perturbations
  are quantized as gravitons, i.e., as another quantum field
  theory like the gauge bosons of the other fundamental
  forces in nature. This is a perfectly good effective quan-
  tum field theory; nothing in principle forces us to aban-
  don this picture until energies near the Planck scale.

They also say that while their starting point was being very different from the holographic picture:

  we find that the models have a range of free parameters,
  and in some parameter regimes become indistinguishable
  from standard virtual graviton exchange

Some of this will necessarily by driven by the need to be compatible with General Relativity in the weak field limit. They are not compatible with strong gravity in General Relativity at present.

So while the idea is kinda interesting, I think they are putting the cart before the horse in asking what their model says about things like the interaction between gravitation and entanglement. That's simply unmeasurable by experiment right now whereas the very-well-understood relativistic precession of Mercury's perihelion is completely out of scope for this initial paper.