You have a theory - "quantum mechanics without wavefunction collapse" - in which the whole of reality is supposed to be equal to a single big object, the wavefunction of the universe. There are various mathematical facts about that object: the existence of various sets of basis functions, the dynamical process of decoherence, and so on.

Now a questioner says, "OK. You say that there are multiple copies of me inside the wavefunction. Is that because there is one of me that splits into many, or were there just parallel mes living separate but similar lives?" You've implied that the answer depends on the definition of something. Can you tell the questioner what definition of self leads to the different answers? So far you've used the example "| / > = | | > + | _ >", which doesn't tell anyone whether they should think of themselves as "/", as "|" and " _ ", or otherwise answer the question. It illustrates a mathematical fact about wavefunctions, not a fact about how to find yourself in them.