[WGSW-24040HP] Does WGSW-24040HP4 support 360-watt PoE power budget from port1 to port12?

No, it doesn’t.
The WGSW-24040HP4 supports 440-watt PoE power budget totally, but the 440-watt PoE power budget is separated by two 220-watt power supplies.
The first 12 PoE port power comes from one of the 220-watt power supplies while the last 12 PoE port power comes from the other 220-watt power supply. Thus, the first 12 port PoE power output cannot be over 220 watts.

We suggest you move some PDs to the last 12 PoE port to prevent PoE power overloading.