The whole point of Bell’s inequality is that quantum entanglement is fundamentally different than classical correlation between two objects which have some opposite properties the observer simply does not know about before observing one of them.
It’s not helpful to use an analogy which teaches the reader the exact opposite of the point you are trying to make.
Your example with decaying atoms suffers from the same misunderstanding. Quantum entanglement is not about lack of information about some specific states, if that was the case, why would anyone talk about loss of locality?
Understanding entanglement and Bell’s inequality requires a completely different ontology than your everyday experience with classical objects. I highly recommend the video I linked above for an approachable explanation. It is not as simple as these analogies but at least it gets to the actual point of this result which tells us something profound about how nature works.
The many worlds interpretation is analogous to global hidden variables, and while out of favor, perfectly consistent with modern physics. That said, the core issue is IMO only a one dimensional property was correlated which hides a lot of the oddities involved.
https://en.wikipedia.org/wiki/Bell_test though none of them are quite definitive on their own https://en.wikipedia.org/wiki/Loopholes_in_Bell_tests. I wouldn’t read much into the loopholes, but they do demonstrate just how difficult this stuff is.
An analogy I like for entanglement is to picture two atoms that will both decay at the same time. You could place them on other sides of the planet and until one is observed to decay nobody learns anything because the timing is unpredictable. After the observation people agree with that timing independent of distance but can’t communicate anything because the timing was random. Still, having two people both knowing some fact at the same time which can’t be observed by outsiders is a useful in it’s own way.
What I like about this is it’s clear what’s going on is different from what’s being described, it’s describing a property of something, and it separates information from communication. On the other hand it’s got plenty of it’s own problems.