I grabbed the "ESP32-POE Ethernet event usage" sample from OLIMEX's Github (https://github.com/OLIMEX/ESP32-POE/blob/master/SOFTWARE/ARDUINO/ESP32_PoE_Ethernet_Arduino/ESP32_PoE_Ethernet_Arduino.ino), and Arduino board manager is using the Espressif ESP32 board definition 2.0.13 from the official Espressif repository.
Sample compiles and runs, never shows that the board successfully gets an IP address despite my DHCP server saying a lease was issued, and I can ping the ESP32-POE at that IP, however the SYSTEM_EVENT_ETH_GOT_IP event never appears.
Use the built-in the ESP32 package demo instead the one we shared, go to File -> Examples -> (under ESP32 library tab) Ethernet -> ETH_LAN8720
If the issue remains it can be a problem in the ESP32 package for Arduino, or networking issue in your network or network equipment.