Thanks for this. I had no idea a ESP32 board with built-in PoE existed. I've been using a PoE to micro-USB adapter to power a ESP board. While it works, the adapter just doesn't look very clean when mounted on wall.
There are a few; the wESP32 [1] is the nicest I've used but the Olimex ESP32-POE [2] is widely used too.
The maker of the wESP32 also recently released a neat RP2040 based PoE solution you may be interested in: the RP2040-Shim [3] to match the already-existing PoE-FeatherWing [4]. Together, they're a small, neat solution.
(Not involved with those products, just found them well-designed/interesting.)