Copenhagen seems to imply that it [interference] cannot occur on any scale larger than a human observer.

[...]

I am far from an expert on fundamental physics, but I seem to recall someone once pooh-poohing the notion that QM and Copenhagen are in any sense tied to human observers

Copenhagen implies that under some circumstances, interference stops. That's all that can be meant by "collapse". Maybe above some length scale; maybe above some critical mass; maybe above some number of interacting particles -- it's fuzzy on the details. And of course, if that scale happens to be larger than, oh, say, a person, then you are branching and then having your branches destroyed all the time.

So yes, if everything is allowed to interfere as naively implied by the Schrödinger equation, you're not talking about Copenhagen, you're talking about MWI.