Is there a difference in nuance between this and ”Nu mi-e frică”? Like pointing out ”I am not afraid”?
I think a native speaker would leave out “mie” most of the time.
It's useful as a contrast to other people. Like if you were in a group and the other people said they were afraid, you'd say “mie nu mi-e frică”. It adds emphasis, but on the person.
If anything, this sentence puts more emphasis on the person, like "I am not afraid".