Tbh type 52Ds is already as capable if not more so then any others in its class. Upgrading it should be lower priority then just building more, as they are likely to operate in squadrons having a larger quantity will be more advantageous then individual prowess.
It's all about sidelobe control. A ship can detect another ship passively through its radar emissions even if the detecting ship is not directly shown upon. That's because the detecting ship is detecting the other ship through the sidelob emissions of the other ship's radars. Sometimes this detection is achieved over the horizon via atmospheric ducting, surface wave propagation or sky backscatter. That is why the ship's ESM equipment is so important, as well discipline in the use of radio and radar.
Mechanical radars, especially those using dishes are prone to having more sidelobes than those using phase arrays and electronic beam steering, although the latter isn't completely zero on it. But you want your side lobes to be as weak so it can't be detected under long ranges.
Another problem is that the older radars use vacuum tube type amplifiers, like TWTs, Klystrons, magnetrons, cross field amps, require a state of high power to operate. The high power of their radar emissions makes it easy to stand out in the background making them detectable. The trend in naval radars is to use solid state transmitters to allow for low power, or low probability of intercept transmissions. This can be applied to traditional mechanical radar designs.
In a ship that has combined mechanical radars and AESAs, the AESAs with solid state transmitters and electronic beam steering can have LPI emissions and ultra low sidelob emissions, making the ship undetectable via enemy ESM. That is until it starts to use on of its traditional radar systems. Such is the case of the 052C/D where you have AESA combined with mechanical radar systems. In later batches, we don't know if the later versions of the mechanical radars onboard the ship has shifted to using solid state transmitters since this is impossible to tell from an external physical point of view.
Ideally you want the ship to be completely AESA and whatever is left to be using solid state. With this, you get the idea why the 055 is what it is, and why the ship uses AESA on just about everything except for traditional SATCOMs and the CIWS radar. But even those I expect to be changed to using AESA in future batches such as the CIWS with the AESA like you see on the Fujian that might be the new standard for the PLAN.
A single radar noisy ship can spoil an entire naval formation trying to be as passively stealthy. So ideally you want your fleet to be as passively undetectable as possible. Ideally you want as much AESA with LPI to be used as possible. If that's not attainable for practical reasons, then mechanical radars upgraded with solid state transmitters for LPI. I have the suspicion that the PLAN is already silently upgrading its legacy fleet, such as the 054A to using solid state transmitters. During ship maintenance we have seen 054As having their search radars removed and replaced though the replaced ones are still physically identical to the previous.
No
Remember that an AESA radar can also act as a CEC datalink and also EW jammer, like with the F-35.
It's a matter of programming the different software modes
Yes but I don't think the PLAN uses it that way ship to ship. That's why the 055 has a set of dedicated CEC arrays that also appears on the Liaoning (retrofitted), Shandong, Fujian and the 075s.
The 055 also has a pair of huge arrays on the side of the ship, which have to be dedicated EW arrays. These arrays also appear on the Fujian's island. This is indicative that the PLAN doesn't use its AESAs for EW.
An S-band AESA can't be used to jam a missile using an X-band guidance radar. The wavelengths are so far off its like a couple of ghosts passing each other. To have a successful jamming, the wavelengths must be of the same wavelength, and of the same phase. To know the wavelength and the phase, you need your ESM to read the threat wave, make a copy of it so your jammer can make a duplicate of it. Defensive jammers are primarily meant to operate at threat radar wavelengths, and in the case of ships, those against the active radar seekers of antiship missiles, which primarily works at the X-band.
As for the CEC, I think the PLAN works on the C-band, which is shorter than the S-band. The C-band allows for a higher information density than S-band, which is the same reason why you see S-band on 4G networks but C-band on 5G. That's the reason for using separate arrays for the CEC.