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First, I did not say local, I said that MWI has no action at a distance. The (nonlocal) connections you talk about are changed locally.
Operators are very far from reality. Ontology is the wave function, quantum states, not values of observables. According to my picture in your language tables are as GRW-m, only there are no collapses and density measured inside a “world” which is a vague concept which has to be carefully explained. These are LOCAL properties of the Wave Function.