I think what I, and others, are having an issue with is the following.

In many worlds, the different branches come about, because after a measurement, the wavefunction is a superposition of different states, each with its own outcome of the measurement, and these states, for all practical purposes, do not talk to each other, because of decoherence. Prior to the measurement, all kinds of interference effects happened, but at that point the wavefunction did not separate into different branches, and there was no meaningful way to talk about different universes or worlds.

Now, for quantum computation, you rely on interference effects. You don't want them to be tiny. So it is precisely what prevents you from talking about separate branches of the wavefunction that is responsible for the speed-up that you want. This is why it seems to me that it is misleading to explain the speed-up of quantum algorithms in terms of parallelism. On the contrary, the speed-up comes from that the wavefunction cannot be separated into different branches.

You are not getting extra compute from different universes. You are getting it because the way the wavefunction evolves mixes everything together in an unseparable way, making use of the whole Hilbert space effectively, rather than dealing with the very specific case of different branches that have decohered. I don't think this is semantics. If you cannot even approximately identify different branches of the wavefunction, while the computation is running, how can you talk about different universes?

Another way to put this is to ask, how is it possible to get an exponential speed-up when comparing a quantum vs classical algorithm? Correct me if I am wrong, but this is what happens with Shor's algorithm. If all it came down to was parallelism, the speed-up would scale with the number of different branches of the wavefunction, would it not?

I still think Wolfram Physics is a more complete theory than Everett's with world histories branching and MERGING.