I doubt that Turkish territorial expansion is a goal of Erdogan's.
On Crete, German paratroopers and air crews took the brunt of the punishment -- but Germany had the island in 12 days despite being badly outnumbered. Churchill's shift of British resouurces (and loss of 12K POWs) delayed the German defeat in N Africa and by more than a year, and slowed down the outcome in Europe as well.
Erdogan is a mystery; perhaps he really does want to reassert Turkish dominance ala Ottoman Empire in the greater region. The Turks ruled for centuries and were only held back by a few Catholic ruled countries.