If this hypothesis is true, would it give us a way to distinguish many-worlds vs. wave function collapse? If the many "worlds" are all interacting with a single classical spacetime, we should be able to measure the gravity of other worlds, right? I'm not a physicist, but that sounds a lot like dark matter to me.
There is no implication that the classical spacetime wouldn’t still split into branches, possibly with different variations in the stochastic effect from each other.
Answering my own question based on Oppenheim's lecture[1]: In his theory, the stochastic interaction between quantum and classical states necessarily causes the wave function to collapse, so it is not compatible with many-worlds. Being able to measure the gravity of other quantum worlds is something predicted by semiclassical gravity, which Oppenheim calls "complete nonsense".
