There’s nothing special about the brain in any quantum theory (except pop science).

In many worlds, it’s not so much that the classical world is an illusion, more that it’s a limited perspective, similar to how the “observable” universe is just a limitation of our position, in both cases the theory is that there’s more beyond the edge that we cannot see (and in both cases we have no way to test that).

I don’t think there’s much difference between many worlds and random selection in the end, at least from our perspective. Either way we experience only state contingent on our state, so any quantum superposition that contains us (ok, sure, contains our brain) we can experience only one concrete resolution to, since the others would require our brain to be in a different state. Many worlds adds “but there is a disconnected copy of us experiencing the other valid states after we entered the superposition”, random chance says “and the other states disappeared when the superposition collapsed”, but without reaching past that horizon of our own state they’re measurably identical theories, so either both equally valid or both equally pointless speculation, depending on how strict you want to be.