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The irreversible “dislocalization of superpositions” over many degrees of freedom (decoherence) is an objective process that leads to dynamically automous “branches”. This does not require any bipartition. However, since this dislocalization does not eliminate the superposition globally, its importance for what we observe can only arise from the locality of observers (the bipartition between them and rest of the universe). Their “subjective individualization” in their locally defined component states is confirmed empirically, and thus avoids an objective collapse as a new dynamical law (which is conventionally located in the measurement apparatus). In the formalism of QT, this individualization (corresponding to a splitting observer in the formalism) can obviously not be explained as a mere increase of information.
There is neither any decoherence nor branching in your simplistic e+p example. So I don´t understand what it has to do with Everett’s branches. The observer’s component states are sufficiently defined in the decoherent branches. In particular, they cannot observe any Schrödinger cats.
Can we leave it that way (whatever else you may have in mind)?