I there any real world empirical support for latest supergravity “theory of everything” hypotheses, or is it all still just speculative math proofs?
This is a brief outline of the development of string theory,
It’s all speculative, in the sense that to date, there are no experiments that string theorists can point to and say, “Look, here’s experimental evidence that supports our theory.” I’m not a string theorist, but there’s a bunch of them working downstairs from me, and you can bet that I would have heard of it if there was (I doubt that they would shut up about it.) 
There’s an interesting quote from Richard Feynman, circa 1982: “[String theory] does make a quantitative prediction… It requires that we live in ten dimensions. Is it reasonable to have a theory that requires ten dimensions? No. Do we see those dimensions? No. So it rolls them up into tiny balls or cylinders too small to detect. So the only prediction it makes is one that has to be explained away because it doesn’t fit with observation.” From today’s perspective, this is a little harsh; there were some papers that came out in the mid-80s that showed that this “compactification” of the extra dimensions could potentially give rise to things we see in the real world, such as the existence of three generations of quarks and leptons. But it’s still fair to say that the results that drive string theory research these days are mathematical, not experimental.
To be more precise, there is no case of something being unknown before string theory, predicted by string theory, and then subsequently confirmed experimentally, which is the real test of a theory. There are “predictions” made by string theory of things which were already known, but these are relatively uninteresting because the theory was tuned to match those things in the first place. And there are other predictions made by string theory of things which were not previously known, but they’re uninteresting because (so far, at least) they’re all things which we cannot currently experimentally test and do not expect to be able to for a very long time, if ever.
Because of this failure to make confirmed, new predictions, “string theory” should properly not be called a theory at all. More accurate would be the term “string model”, or “string hypothesis”. It’s nowhere near the lofty scientific heights of the Theory of Universal Gravitation, or the Theory of Evolution.