[segment-explorer] Signal updates to React (#80316)
We never actually invoked the listeners attached by React. Updates only worked on soft-navigation because we also re-render the DevOverlayRoot and don't bail out anywhere at the moment.
Just invoking the listeners is not sufficient after https://github.com/vercel/next.js/pull/79699 since userspace and dev-overlay would read different versions of `listeners`. I ported the segment explorer into the new folder structure. Updates now flow through the `dispatcher` and then invoking the listeners actually works. Though mid term we should move the segment tree into actual React tree to get rid of the sync updates.
I also noticed that we're missing an implementation for a remove operation which is required to show the correct state during soft navigations.
