Synchronous rectifier design for isolated high power PoE+ (802.3 at and bt) applications can help increase efficiency and reduce heat.
The ESP32 may be a low power chip when compared with other WiFi or networking chipsets in the domain. But in conventional terms, ESP32 is not exactly a low power …
A quick rule ot thumb to pick an EE type SMPS flyback transformer core for power output in the range of 1-100 watts.