No need for separate Movie or TV show picker screen, use a menu item that pops up when hitting start rename
This also means all the rename navigation can be collapsed into a single detail view. Should help NavigationSplitView to better understand what is going on with the current state. Can still have separate view structs to maintain separation of concerns, but they'll ultimately tie back to the same navigation view.
Some kind of flow should enable going back and forth between the primary rename screen and the summary view. Maybe a back button, maybe a toggle state.
Make it easier and more clear how to exit the rename flow without performing any actions. It should get you back to the plain detail view of the addition you were renaming.
Reviewing with users, a couple things came up about edit-ability: