Decoherence of a system happens when the entropy of entanglement is maximal, so if you want a formula then it's S(Tr_a(p_ab)) -> N/e. In practice a complex system is probably never fully decoherent, but the separability is small enough to not matter; if we're being truly rigorous we work with it as a limit, similar to how we use the "classical limit" in other parts of QM or other contexts.
(Analogy: imagine saying "Relativity doesn't explain how we live in a Newtonian world. If relativity is valid, it should be able to say at exactly what speed motion becomes nonrelativistic. Provide a formula for it")
Relativity is a real formula, you just say that decoherence seems to correlate with entropy and then gave a formula for entropy. We don't have a formula for decoherence. Any explanation for decoherence that doesn't help us find a formula for it is nonsense.
Here is a better theory than MWI: We live in a simulation, the computer is optimized so when there are too complex interactions in an area it simplifies the state into some probable untangled version. This theory predicts that decoherence thus happens at certain computational complexity levels, that is something we could try to find and test experimentally making this theory more scientific than MWI. MWI doesn't lead anywhere, it isn't science, it is just nonsense. I'm not saying my theory here is a good one, but it is better than MWI which isn't a high bar.
Relativity is a real formula and the classical limit is a real phenomenon, but there's no formula for when a relativistic situation "becomes classical".
> you just say that decoherence seems to correlate with entropy and then gave a formula for entropy
If the observed system and the observer/external universe are fully entangled (i.e. their entropy of entanglement is maximal) then decoherence has occurred and all observations of the observed system by that observer will be indistinguishable from if the system were not in superposition. That is a mathematical fact that falls right out of the equations. So I don't know what else you're asking for.
(Analogy: imagine saying "Relativity doesn't explain how we live in a Newtonian world. If relativity is valid, it should be able to say at exactly what speed motion becomes nonrelativistic. Provide a formula for it")