If all conjecture is stripped away - to the absolute basics - why is a black hole deemed to be massively dense, rather than massively empty wrt its environs?
I am not sure what the "massively empty wrt its environs" means.
There is a lot of conjecture, because we are not able to closely inspect even the things we can see, such as White Dwarf Stars and Neutron Stars. So, much of their properties are based on subatomic physics experiments and associated theories.
If we accept that neutron stars exist in the form of all baryonic matter in them having been so compressed that it all turned into neutrons, then we have "stars" that are "dead" in that they are not producing more energy by nuclear fusion, and they are only several miles in diameter, but pack in the mass of up to a few of our Suns.
That isn't quite enough mass to produce an "event horizon" where the escape velocity from or above the surface of the mass exceeds the speed of light. But, pack in some more mass, and you do get an event horizon, so it is then a "black hole".
We can't see anything inside a black hole. so we really don't know if what is in there is just a bigger neutron star, or something that collapses to even greater density than neutrons. The current speculation is a "quark-gluon soup". There is even some speculation that the centers of large neutron stars that are not massive enough to be black holes have already had material in their centers transform into this "soup".
So
maybe what is inside a black hole is a "Quark-Gluon Star" that is not much smaller than the event horizon for low mass black holes.
But, that is where conjecture completely takes over, because we can't see anything in there and the Theory of General Relativity apparently breaks down at the event horizon.
Some quantum theorists think that there is something more dense than a "quark-gluon soup", but quarks are also theorized to be "primary particles" that can't break down into something even smaller. So, what else is there?
Some theorize that all matter turns into energy at extreme densities. But, does that energy still have mass? If not, then wouldn't a black hold suddenly lose its gravity? Would that be a "big bang"?
Conjure away - nobody really knows!