Im not sure you can claim that it has a better payload than Type 054A/P. The turks will likely use Atmaca which is the same class as. C-802A/C-803 which we know the type 054A usually holds 8 as well. The 054P uses CM-302 which is a much larger missile with more speed and range and this is likely why there are only 4 (not sure if they could hold 6-8 total and PN just doesn't have the funds to do it or their is a weight limitation).
The AESA you are referring to is the SR2410C?
This replaces the Type 382. The benefits of this is that the AESA are far more resilient against electronic warfare and can be used for detection, tracking, and a redundancy guide weaponry to target. Yes the SR2410C can act as the fire control to provide weapons guidance in the event that the there is damage or jamming to the type 344 or MR-90 radars.
Compared with the Type 382 radar, the overall performance of the SR2410C is better. Although the SR2410C has no difference in the detection range, its information processing capabilities and multi-target tracking capabilities have been improved over 382