In that link that says that was Everett's initial attempt to solve but it has been debated and extended. I only have a podcast understanding of it, and have heard the popular proponents of many worlds like Sean Carrol say that is the biggest problem that needs more development, he has his own self-locating thing but there are many other approaches.

But on the other point, how can there be an irrational number of branches to sample these statistics from? I just can't visualize the type of structure that would have that but I'm sure it is more subtle. I've heard the branches aren't branches under MWI but instead are something more continuous and I guess I don't understand it at that point.

Wikipdeia references https://arxiv.org/abs/0905.0624 and first thing I noticed in section IV the author incorrectly calculates copenhagen prediction (because probabilities are counterintuitive), but correctly everettian prediction (because marginal outcomes are obvious there) and claims this discrepancy disproves MWI, he conveniently forgets about empirical equivalence of interpretations, so that it's easier to make an error and get different predictions. Then makes incorrect claim about MWI. Any given observer will probably observe confirmation of Born rule due to the law of large numbers.

The structure of superposition is given by solution of the Schrodinger equation. It's often continuous, e.g. electron's s orbital in atom is a continuum of coordinate eigenstates. In this case a discrete sum is replaced with an integral and Born rule becomes a function on this continuum, but a discrete case can be easier to understand, so I recommend to start with that. The proof follows the law of large numbers https://en.wikipedia.org/wiki/Law_of_large_numbers