I’m pretty sure this goes against the properties proven of entanglement (Bell test) and how far entanglement can propagate, but I don’t know enough about quantum mechanics to explain why this explanation is incompatible with entanglement.

If you don't know anything about the topic then maybe you shouldn't speak on it. Especially when claiming you have debunked peer reviewed papers from Harvard physicists like Jacob Barandes.

However, I don’t currently see how this at all explains computing with superpositions; if it’s just statistics a superposition can never exist

Superposition is a property of statistics. Even classical statics commonly represent the system's statistical state as a linear combination of basis states. That's just what a probability distribution is. If you take any courses in statistics, you will superimpose things all the time. This is a mathematical property.

so entanglement doesn’t exist; so quantum algorithms wouldn’t be possible, but we know they are.

Quantum advantage obviously comes from the phase of the quantum state. If you remove the phase from the quantum state then all you are left with is a probability distribution, and so there would be nothing to distinguish it from a classical statistical theory. But the phase is, again, a sufficient statistic over the system's history. The quantum advantage comes from the fact that you are ultimately operating with a much larger information space, since each instruction in the computer is a function over the whole algorithm's history back to the start of the quantum circuit, rather than just the current state of the computer's memory at that present moment.