Pi has nothing to do with our universe or the way it is tuned. It's more fundamental than that. It would be the same value in any universe. You don't need ci

Pi has nothing to do with our universe or the way it is tuned. It's more fundamental than that. It would be the same value in any universe. You don't need circles, or Euclidean space, to discover Pi. It arises in all sorts of pure mathematics that have no direct connection to physical circles. That said I suspect you are right that we gave a name to it because it comes up so obviously in our experience.