"Sylvnas" book. Is this an error?

This is precisely it. Some of the mages of Dalaran are from the common stock/low level nobility. I am sure they would have liked to talk about the amazing things they learned/scare their own non mage children/friends.

Unless it’s stated somewhere that that’s what happened, it’s just speculation and headcannon

Its canon, with one n.

Regardless, Khadgar said it is an old legend of Lordaeron. Not just a legend among mages.