Indeed, that's one reason to be highly skeptical of that study. The "cosmological coupling" doesn't make sense in the context of general relativity. The global scale factor is not locally even a thing. In certain cosmological spacetimes, the scale factor isn't even uniquely defined globally.

The authors motivate the cosmological coupling by citing the behavior of black holes placed in otherwise homogeneous universes. Such black holes grow over time, but they grow by accreting the surrounding fluids (which are present due to the assumption of homogeneity), not by magically eating the scale factor, as the authors seem to suggest.

The only interpretation of the black-holes-as-dark energy idea that might make sense relativistically is that black holes have a negative-pressure coupling to other black holes. Then as the black holes separate from each other due to cosmic expansion, the negative pressure feeds them mass. This achieves the same outcome without positing a magical coupling to the global expansion factor.