I think Mab is well aware that Harry is starborn as well as a wizard ...
Indeed!
I think Mab knew Harry as a Starborn wizard from his birth. I think that is WHY she interacts with him at all, and the entirety of her intention toward him.
His mom was well-known to the upper echelons of Winter. Bargaining with the Leanansidhe -- Mab's Right Hand -- to be Harry's
godmother? The Ruby Waystone? These are not small matters! Harry's birth was well-known to Winter; Harry's wizardly potential as Margaret's child, his Starborn potential from his birth-circumstances... obvious to Winter.
But if his Mom's preperations were not small matters, neither is Harry a "small matter" -- a Starborn wizard never is! As an apprentice, he defeated one of the most-mighty Outsider Knights there is. How big a deal is that, really?
Well... when the cadre of WC refugees arrived (and settled the Molly case in favor of a Doom over her and Harry), we learned that the Outsider assault would have likely taken them all (if not for Michael); and who was the wizard fighting those outsiders? The Blackstaff, the WC's most dangerous and deadly combatant. And apprentice-Harry was punching in
that weight-class.
To be brutally frank -- Mab
NEEDS that kind of power to be part of the defenses of the Outer Gates. Therefore, she needs
Harry.
All of Mab's interactions with Harry -- including making him Winter Knight -- are about making him a better, stronger wizard, so he can fight the Outsiders better.