Level 3 universes have the least to do with string theory, but of all the types of parallel universes, Level 3 universes have most captured the imagination of popular culture, spawning their own genre of science fiction and fantasy: alternate history.
These are stories written with settings that are based on our own universe, but with the assumption that some historical event went differently, resulting in consequences different from those in our own universe. (For the non-science fiction fan, think of It’s a Wonderful Life.) In these fictional universes, it’s possible (and common) that visitors from one universe can interact with a Level 3 parallel universe.
Obviously, in these fictional universes, the author (and reader) care about the macroscopic differences, but the many worlds interpretation applies to all levels. If a particle decays, or not, different worlds represent those events. No one observing would be able to tell the difference between them. However, if they were observing with a Geiger counter, which detects radioactive decay, the quantum split would result in further splits.
The Geiger counter is triggered in one universe and not the other. The scientist who detects the decay would react differently, perhaps, than the one who does not detect the decay. So, in principle, this is how these tiny quantum universes become full-fledged parallel universes.
In fiction, the effects are generally more dramatic, such as the southern states winning the American Civil War or the Byzantine Empire never collapsing (both of which have been explored by alternate history author Harry Turtledove, called “the Master of Alternate History” by his fans).