what sort of experimental constraints are there on the scale of spatial structure like that
By AWT this constraint doesn’t exist, but here are less or more significant conceptual limits. For example the rest mass of photon appears zero, but when the wavelength size of photon becomes comparable to observable Universe, the photon cannot move inside it furthemore. After the energy of photon becomes equivalent to its rest mass. Such mass appears low (~10 E-61 kg), but here are even stronger limit. When the wavelength of photon becomes comparable to wavelength of CMB, every photon dissolves in CMB noise, which corresponds the graviton noise of previous Universe generation. By such way, the minimal rest mass of photon is quite large, but it’s limited by observability of photon, not by existence of photon as such.
If some civilization could have look inside of large black hole, he would probably see the same things, which we can observe around us, but it would probably dissolve, if it could visit us. But such civilisation can construct a giant microscope, as large as whole black hole and it can use focused gravitational waves to observe the life inside. After then such civilization could see more, then the single generation of Universe because of tunnelling of information through event horizon. Therefore the observational limit is just a matter of observational scope, by my opinion.