When working with multiple branches, it is currently really difficult to know which branch / tag the given file has which can have dangerous effects, especially when it is so easy to accidentially remove a sticky tag from files because IDEA remembers the previous selection.
I think you should at least have an option of showing the current sticky tag of the file in the project view right after the name of the file. The color of the font could be gray to make it as unintrusive as possible.