> How does a particle keep track of how many other entities it's entangled with and in what ways? Where does that information live? [...] A complete explanation would answer all of these questions - and others - with ease.
I disagree with this framing. Fundamental laws of physics are always going to have unanswered questions of this type. Given any set of rules you can ask "But what explains those rules? What are they built out of? How are they enforced?". Sometimes those questions will have answers and lead you deeper, but for truly foundational laws you'll be wasting your time. It'd be like asking "Where is the true platonic number 2 located? Is it in Canada?".
You can ask the same questions of classical mechanics, of course. We tend not to because it agrees with our intuitions, but you can. For example, where would a classical particle store its velocity? For that matter, where would it store its position? It's circular to say it stores its position where it is! Clearly a "true" theory of classical mechanics would answer these very important questions.
Concretely, there are a variety of ways of writing programs that act like quantum mechanics, that differ wildly on how the state is represented. This detail is simply not pinned down by the postulates of QM. That being said, what all these programs do have in common is that they are actually tracking information related the state; that the state is ontic.
So pick your favorite state representation: state vector, density matrices, Feynman paths, whatever, they all work! That doesn't mean they're describing things that aren't real, it just means there's many ways of correctly describing reality; such convenience!
I should probably add that I know everything I've said isn't convincing to a skeptic. Ultimately it comes down to: I know I can think of the quantum state as being really real, and that will work totally fine. I find that style of thinking is effective for me, and intuitively compelling, so I do it.
Every once in awhile I'll run into someone pointing out the philosophically fraught underpinnings of assuming reality is real or whatever, and I basically won't care because my goal is to be effective; not to be Descartes-level-certain about everything.
An example of something that would make me care is if QBism contained some key conceptual trick that made problems easier, and gradually many papers started using it because of this advantage. Or, of course, if there was an experiment distinguishing between interpretations.
I'm aware of the distinction.
> How does a particle keep track of how many other entities it's entangled with and in what ways? Where does that information live? [...] A complete explanation would answer all of these questions - and others - with ease.
I disagree with this framing. Fundamental laws of physics are always going to have unanswered questions of this type. Given any set of rules you can ask "But what explains those rules? What are they built out of? How are they enforced?". Sometimes those questions will have answers and lead you deeper, but for truly foundational laws you'll be wasting your time. It'd be like asking "Where is the true platonic number 2 located? Is it in Canada?".
You can ask the same questions of classical mechanics, of course. We tend not to because it agrees with our intuitions, but you can. For example, where would a classical particle store its velocity? For that matter, where would it store its position? It's circular to say it stores its position where it is! Clearly a "true" theory of classical mechanics would answer these very important questions.
Concretely, there are a variety of ways of writing programs that act like quantum mechanics, that differ wildly on how the state is represented. This detail is simply not pinned down by the postulates of QM. That being said, what all these programs do have in common is that they are actually tracking information related the state; that the state is ontic.
So pick your favorite state representation: state vector, density matrices, Feynman paths, whatever, they all work! That doesn't mean they're describing things that aren't real, it just means there's many ways of correctly describing reality; such convenience!