https://onemileatatime.com/news/anadolujet-rebrand-ajet/

Looks like the business model will be more or less like QF and JQ where both airlines have the same owner but act independently and can even compete on the same route.

I guess TK realized that they cannot compete against Pegasus ex SAW/ESB without significant cost cuts.

If they follow the QF/JQ model, E/E+ should still have some limited perks on AJet (if memory serves QF Plat/Plat+ have lounge access on JQ).