Cresent moon was used by Turks before the Ottoman Empire, the Göktürks used it, the Uyghurs... cresent moon was used by many people throughout history.
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Lots of historical revision going around that the Ottomans adopted when they took Constantinople in 1453. When the Ottomans long before 1453 used Crescent banners. The Ottomans used wide range of flags before adopting the current Crescent and star in the 1800s as an official flag.
As you said the Turkic peoples used crescent symbol as a symbol long before they became Muslim and long before the Ottoman Empire.
Greeks just engaging in stupid historical revisionism. If the crescent is a greek symbol how come they dont use it? Ironic isnt it.
Also the swastika is not Greek. Greeks claiming everything is Greek.
Eagle banner also has nothing to do with Greeks as many cultures and civilisations adopted the eagle as a symbol in coat of arms and in flags.
The Turks even used big cats as their banners and wolves.