Could be all of the above, in terms of types: physical interstellar, physical trans-temporal, physical multiverse, non-physical of those same mediums, and other unknowns, ranging from god-like power to just a little more advanced than we suspect ourselves to be. One variation of the soon-to-be-evidenced multiverse theory allows for a multitude of neighboring universes having their own physical laws. If this version of the multiverse theory is true, literally everything that shouldn't exist, does exist. The more truncated multiverse theory allows the existence of everything that conforms to physical laws.

I have a problem with the multiverse theory, though; why haven't I been visited by the infinite hordes of self copies who were all capable of doing so, while desiring to do so? In a multiverse where everything that can exist does exist, this should have already occurred for everyone here.

I think it's more likely we're in a sort of petri dish. From time to time, a "whistleblower" makes a claim that humanity would NOT want to know the grim truth about the universe and our existence. Some have even suggested the "secret space program" abandoned Star Trek-like deep space exploration, 'because there was no real point'. Could take that to mean we can now travel without even leaving our present location (multiverse) or that we would be an artifice exploring an infinite 'hamster wheel' construct for no good reason.