There is no mystery. Realism requires object permanence, and object permanence requires that you believe in counterfactual statements. If I measure something at t=0 and t=2, I could have measured it at t=1, and so you have to believe it had a value at t=1 or else you devolve into solipsism. If you believe an objective reality exists at all then you have to uphold these kinds of counterfactuals or else you have no basis to believe that objective reality exists independently of you measuring or observing it.

Bell’s theorem proves clearly proves that special relativity simply lacks sufficient structure needed to give a realist account of the world. Special relativity is not compatible with objective reality. Rather than accepting this conclusion and admitting special relativity needs additional structure added to it, physicists almost universally came to the consensus that we should reject the very idea that there exists an objective reality independent of observation to preserve the sacred status of special relativity

This became the dominant Copenhagen interpretation. Physics is just about what shows up in measuring devices, during observation, not about objective reality. Many Worlds then showed up later as a cope. It arose as a middle-ground by arguing the mathematics used to predict what shows up on measuring devices is objective reality, as if we live in a Platonic realm of mathematics given by the idealized state vector in infinite dimensional Hilbert space.

This coping mechanism is not even coherent. You can’t derive an “ought” statement from a lot of “is” statements. The conclusion can never be stronger than the premises. Similarly, you cannot derive observability by starting from pure mathematics where nothing is observable. Many Worlds has no algebra of observables and it is logically impossible to derive them. You must begin with objects defined in terms of their observables and fit models to their dynamics. You cannot logically start from the Platonic realm of pure mathematics.

It is just a coping mechanism to avoid questioning the completeness of special relativity while also saying you don’t deny objective reality by turning the pure mathematics into objective reality.

If you just admit that a contradiction between special relativity and objective reality means we should call into question the completeness of special relativity, then you can add a little bit of additional structure to it, something called a preferred foliation, and then you suddenly discover that you can fit relativistic quantum mechanics to a realist theory of point particles moving deterministically in 3D space with well defined values at all times independently of the observer.

The theory suddenly becomes intuitive and clear without any mystery, and decoherence was literally discovered through analyzing a realist model of quantum mechanics, because it gives such intuitive clarity of what is going on it finally looks like you are analyzing a coherent physical theory and not an incoherent mess which only has something to say about what shows up on measuring devices.