SR is the model of fixed continuous space-time (and the "inertial frames of reference" are defined only in such model). Thus the SR is applicable to the reality only as much as the real space-time can be approximated by such a model. That approximation is pretty good usually, except at the very large scales (the non-fixed, expanding, nature of the real space-time starts to show more than negligible deviation from the SR model) and at the very low scales where the non-continuous nature of the real space-time starts to play a role.

>“anti-de Sitter” (AdS) space. In these warped worlds, spatial increments get shorter and shorter as you move out from the center.

and that sounds like the metric is p-adic there. While our typical Cartesian coordinates express the metric naturally produced by the real numbers, at large scale the world may have different metric. Our 46B ly radius visible Universe's Schwarzschild radius is about 10B ly, so if we go about 160B ly beyond the visible Universe border - we "can" do it as otherwise the Earth would be the "center of Creation" - we will have the 200B ly radius Universe which is inside its own Schwarzschild radius equal to those 200B ly - so our visible 46B ly radius Universe is basically inside that large black hole and at that scale the space seems to be AdS.