I've been dabbling in physics/QM for just a few years, and was reading "The One: How an ancient idea holds the future of physics" - my interest was piqued because I've read quite a bit about Neo-Platonism, and this philosophy, extremely influential historically, holds to the concept of a transcendent first principle or absolute "One." Okay, to the point - the author Heinrich Pas, who holds a pretty serious academic position in Germany and the book is praised on the cover by Hossenfelder - insists that the primary idea with Everett's interpretation of QM, popularized as "Many Worlds," is that what underlies our universe is a universal quantum function.
He says Everett himself did not like the emphasis that others put on the possibility of parallel universes. Everett is quoted (p.79) in an interview as saying "The question is one of terminology: to my opinion there is but a single (quantum) world, with its universal wave function. There are not "many worlds," no "branching," etc., except as an artifact due to insisting once more on a classical picture of the world. Pas says that in the Everettian view, held by Zeh and others, the most fundamental reality is the universal quantum wave function, and that our empirical physical universe, leaving aside the question of other worlds, is only derived, less fundamental, less "real."
The physicist Leblond, who interviewed Everett, was quoted "To me, the deep meaning of Everett's ideas is not the existence of many worlds, but to the contrary, the existence of a single quantum one" and "the 'many worlds' idea again is a left-over of classical conceptions in obvious contradiction of Everett's original intent." Pas says "what is typically overlooked is that Everett's multiverse is not fundamental, but rather apparent or 'emergent.'"
So my question is, does the idea of many alternative physical worlds follow necessarily from Everett's interpretation, especially if you are willing to leave aside classical assumptions and entertain the idea that the real fundamental reality is not our empirical world, but a universal quantum reality that lies our experienced world? Personally I have trouble buying the idea that every time my dog lifts his leg to relieve himself, he's creating billions of universes in the process.