Butcher has never explicitly stated what a Mantle is. So a Mantle is whatever we think it is. Such is the beauty of fiction ...
It's pretty clear, though: a "mantle" is a semi-sentient magical suite of powers, motivations/drives, and restrictions. This may not be exactly right, but it's a reasonable approximation. (n.b. there's also the DF RPG; Jim was involved in that, so the "Mantle" there is probably a good game-rule approximation of the novels' use of "Mantle," too)
... And what Eb thinks about it matters not at all. He doesn't choose the holder ...
Ebenezer, as one of the most-senior WC wizards, is an authority on magic. If he calls such-and-such a thing a "mantle," then it probably is (except for the vanishingly-small chance that a technical expert like Eb would use a technical "term of art" in a sloppy fashion when writing for future generations).
And while he doesn't get to
choose a new Warden, the Blackstaff could probably manage -- eventually -- to
kill most any Warden that he disapproved-of strongly-enough (I imagine there's a fair bit of gray-zone between the "
three or four [Eb would] be willing to see take up that particular mantle" and those he'd see as automatically needing removal-with-prejudice.
So it's not utterly irrelevant who Eb thinks should be the Warden of the well on the island...