The difference is that they're not localized. It's only local hidden variables that are forbidden by theory.
One way to look at it is that every one of those pieces of configuration space apply to all of space and all of time. That's not forbidden. But it also means that these values aren't directly accessible. They can only be partially inferred.
This is being downvoted, perhaps because I put a humorous analogy in there, but I really am curious, isn't this what is claimed? The "real" ground truth of the universe is "configuration space", which is some kind of mathematical construct, and which can't be perceived directly but only partially inferred?
I'd like to know more about this since I have never heard of this concept before and I feel like it has far-reaching implications
It's not quite as dramatic as it sounds. It's a somewhat more mathematically sound way of saying all of the usual stuff about quantum mechanics. It just takes the QM side more seriously, rather than trying to describe it as a bag on the side of classical physics.
The unobservable parts are not really any different from indirectly inferred concepts like potential energy. It's just that even seemingly concrete notions like location turn out to be macro scale approximations of this phase space. They're not accessible only because you are a macro scale object. You can very much demonstrate that it's real by simple experiments. You just need to be able to take them seriously, which is unexpectedly difficult because classical physics seems so intuitively obvious.
Yeah I'm honestly not too sure here either, the more I think the more I believe simulation + hidden variables may be the true explanation behind our reality.
How is that different from hidden variables?