Currently you can tell which way it’s connected on the LCD: if it’s WiFi connected, it shows a WiFi icon (the little triangle bar icon); if it’s wired connected, it shows a small network icon (looks like 3 boxes connected via cables).
Yes we can add the indicator to the UI as well.
The reason it can only be done through WiFi is that OTA update for ESP8266 is a standard feature built-in to the core libraries. OTA update with wired Ethernet — no one has ever written that part yet. That said, I have started looking at ESP8266 core 3.x which seems to have unified the handling of WiFi and wired Ethernet, per it’s possible that OTA update can be done with both, but I have to do some research on that.