Perhaps it would have made more sense to develop the Hürjet 20-30% larger with 2 F-404 engines.... Additionally with a small internal weapons bay for 2-3 AAMs and a bit more stealth Design.
As it is now, it would always lose as a future naval version against Russia, China, India or France, e.g. as an aircraft on a carrier.
Without a catapult system, higher payloads are already out of the question, with only one F-404 engine you can't do anything with this aircraft, which is actually a training aircraft, even if you have STOBAR like on the carrier Mugem.
I doubt that Kizilelma as a wingman can somehow compensate for this weakness of the Hürjet as an interceptor if they fly together, the main platform Hürjet is simply 2 Levels too weak compared to a Rafaele M, J-35 & Co.
In a serious conflict where the conflicts will shift to Africa and Southeast Asia, you can't do anything with the current Hürjet as a naval version.