Having GaN does not automatically mean the module is more powerful, it means it has the potential to be more powerful. You still have to pump more juice into it. The main feature if GaN is that it runs cooler, allowing for a lighter cooling equipment, to produce the same rf power as a GaAs part would. A GaN part would therefore be able to take much more power than a GaAs part before it burns out. It does not automatically confer more power. You can have a GaN radar that isn't so powerful but you can reduce the bulky cooling that goes with it and less power needed for the cooling system.
The 052D is still limited by the power infrastructure it inherited from the 052C unless it's generators have been upgraded. I would think the 052D's modules makes more power than the 052C's, being all liquid cooled instead of a hybrid air and liquid cooling (all air cooling limits the power on the Type 45's SAMPSON radar). I do not think the 052D's modules were GaN, at least not from the start anyway. If it were GaN it would begin where the 052D's second batch, where they dropped the calibration field booms off the radars, indicating that the modules have been redesigned so calibration support is now on the module itself, possibly by mutual coupling (extending the size of the wave until it interferes the next element, allowing the elements to read each other's output, and this interference is then measured if it's the correct level). If the modules have to be redesigned, it opens the opportunity that the modules might have other changes.
Hence if the first few 052D has the Type 346A (the first four ships in the 9th Destroyer Division, like 172 to 175), then at some point where the second batch begins (example would be 154 of the 6th Destroyer Division) you have the improved boom less 346A. These improved radars should be called 346A+. The extended 052D should come with this too.
Assuming 346A+ radar now uses GaN, the ship needs to pump more power to the radar to actually see a better performance benefit, and this requires an updated cooling and power infrastructure to the radars. I may think the power infrastructure between the 052C and 052D may have been improved but I'm not too sure between the first and second 052D batches although it's still entirely possible the power is pushed further. But it's nowhere like what you see on the 055 which is expressedly built for that purpose while the 052D hull is one that's already highly pushed to its limits already. The main benefit of using GaN then might be to improve the reliability of the radar modules by running cooler while the power increase might be minimal due to the limitations of the ship. I think the 055's radars are so powerful that it does not need the support of a VHF radar like the way the 052D still does.
I lean towards the belief that the Dual Sided AESA for the 054B, the smaller dual sided AESA seen on the 075, the AESA targeting emitters on the new 054A batch, are all GaN, to allow them to be light, slimmer and less bulked by cooling equipment. It's also possible that many if the PLAN's old style mechanical rotating radars may have been back end upgraded by replacing their cathode ray based TWT or klystron power amps, to one that is solid state using a large GaN power amplifiers, the whole purpose is to improve reliability.