Unless one is simply sorting songs into bins, I don't don't find the question "Is it traditional?" to be very interesting - particularly if "traditional" is in the surprisingly fuzzy technical sense (once) favored by folklorist.

If Y learns song A orally from X, and that song in Y's version is ipso facto "traditional," those facts tell us nothing about the nature of the song itself. They only tell us that somebody once learned the song and perhaps made minor textual and melodic changes later.

Nor does whether it has a known (to whom?) author or whether it's now in the public domain.

The song's the thing, not the abstract slots it can be fit into.