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the total energy of each [world] depends on its probability measure
Please check your sources on MWI. I think you must be misreading them.
Branches may actually interfere with each other in ways that aren't really meaningful, so there isn't really a point where you get total decoherence.
So in reality, decoherence is a matter of degree. But I thought that the existence of one world or many worlds depended on whether decoherence had occurred. Is there a threshold value, a special amount of decoherence which marks the transition?
it sounds like you might have issues with what looks like a violation of conservation of energy over a single universe's history. If a world splits, the energy of each split-off world would have to be less than the original world. That doesn't change the fact that conservation of energy appears to apply in each world: Observers in a world aren't directly measuring the energy of the wavefunction, but instead they are measuring the energy of things like particles which appear to exist as a result of the wavefunction.
Advocates of MWI generally say that a spli...