[a_cardboard_box]

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.

[layer8]

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.

[a_cardboard_box]

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".

[1] https://www.youtube.com/watch?v=sde7k3jJp5E