The |y> superposition of you has one experience, and the |x> superposition of you has a different experience. The |y> version has no information about the |x> e

The |y> superposition of you has one experience, and the |x> superposition of you has a different experience. The |y> version has no information about the |x> experience, and vice versa, because those two states are orthogonal in Hilbert space. This is essentially the prediction that results in the Everett many worlds interpretation. If you somehow had an experience of "both outcomes simultaneously", that would violate the quantum mechanical prediction that there is no mutual information between the two superpositions. There are two brain states, an x state and a y state, and they know nothing about each other. To each brain state (with the limited information available to it) it would appear that something "definite" had happened, even though in the global picture, a superposition still exists.