ESP32 MCUs can be a great replacement for popular ATmega328 Arduino boards, but they are somewhat different. Even if ESP32 Espressif Arduino core is used, some of the libraries will not work out of the box.
Just like EEPROM will not work without changes. Mainly because ESP32 does not have EEPROM memory. An external flash is used instead.
Good thing, ESP32 EEPROM library distributed together with Espressif ESP32 Arduino core solves this problem in a quite nice way. All you have to do is to call EEPROM.begin with a size of emulated storage size in bytes as an argument. From there, everything goes as before.