The most logical option for us would be to build Trakya, but change its design enough to make it primarily a drone carrier, for TB3, KE and Anka-3. We don't need an aircraft carrier that we can't protect, hell, we can't even properly protect Anadolu right now. Only after building all of our projected warships, we can protect it. Not to mention, our options for getting a carrier into any ocean is controlled by other countries, what happens if things change and we aren't allowed to pass? Then we end up with a carrier we can't use on 2 of our 3 seas and we don't really need it for the third. And even if we tried to use it there, we would need to relocate most of our Navy to just protect it.
It isn't an "ambitious" project, it is just vain. We would be much better served if we focused the resources it would require to our submarine and destroyer project and establish ourselves as *the* regional power when it comes to naval power.
That was the first estimate, then it was revised to a billion but its true cost was never revealed.