There is a radar horizon calculator.
Going to assume that the missile is coming at 10 meters height, the 055's Type 346 radars at 17 meters height, while the Shandong's Type 346 radars are at 60 meters height. I don't really know what is the Shandong's radar height for its Type 346 so I am making up that number.
At 17 meters radar height, the target is radar visible at 30 kilometers. At 60 meters radar height, it is 45 km. Let's assume the missile is coming in at Mach 2, or 0.7 kilometers per second. At 30 kilometers radar visible range, you got 42 seconds to react. At 45 kilometers, you got 64 seconds to react.
I don't think Mach 2 missiles are going to come in at 2 meters. That's too fast for too low. Based on some modern supersonics, the lowest I would be willing to go would be 5 meters but 10 meters is more likely. Anything like 2 to 5 meters height should be subsonic.
If a destroyer puts its AESA at 30 meters height, then target becomes radar visible at 35km, for a sea skimming target at 10 meters height, and with a Mach 2 target that would be 50 seconds reaction time. For 35 meters height, that is about 37 km, for 52 seconds reaction time. So the difference of putting the AESA at 17 meters vs. 30 meters is about 8 seconds worth of reaction time. If its subsonic, then at Mach 0.9, that's about 0.3 km/s.
However in reality, ships also have secondary radars that are optimized for searching for sea skimmers and closer ranged engagements. For the Type 055, its secondary X-band AESA on its integrated mast is probably about 30 meters in height. For the 052C/D, the Type 364 Sea Gull radar is probably about 34 to 35 meters in height. For Burkes that are equipped with the SPQ-9B (not all currently are but some), the Spook 9 is about 36 to 37 meters in height. The Type 364 and the Spook 9s are not AESAs but it doesn't matter as long as they do their job. At this point you have to recalculate the actual detection and engagement ranges based on these secondary radars.
In the case of the Liaoning and Shandong, they each have a pair of Type 364 radars and a Type 382 radar that's higher than the Type 346, which further extends the radar horizon. For 003, it has a quartet of X-band AESAs higher than the Type 346s, with its crown mast dedicated to CECs and ESM panels.
There are two other things that can extend the radar horizon on these ships. That's where the ESM comes in. On the 052C/D and 055, the ESM masts occupy the highest points of the ship. On the 055 its the stalk sticking out above the integrated mast. On the 052C/D, its the small tall mini-mast behind the Type 364 radar and goes above it. The extended height allows the ESM to pick up the radar and radio (datalink) emissions of the threat missile as far as possible as their further extended radio horizons allow.
The final thing that needs to be mentioned is how far these radars also use inversion layers or atmospheric ducting. This phenomenon is where density and thermal layers in the atmosphere create a wave guide that refracts radar waves over the horizon. It so happens that the Type 366 radars on the 052C/D and Type 054A employs this principle, copied from the Mineral ME Bandstand radars used with the Sovremennys. The question is to what extent other Chinese ESM and radars have incorporated this. There is also this question if other radars in the West would exploit this principle. Its a situational thing but it so happens the Western Pacific gives those situations.
