Closes#9058 .
Ensures behavior of `_stash_exp` in `exp run` is matched in `exp save` without duplicating logic.
The simpler implementation ended up being worse for maintenance when wanting to make `exp run` and `exp save` behavior in sync.
Allow to include a list of potentially untracked files.
Covers the DVCLive use case where in the first run the generated files won't be tracked in Git yet.