Connecting Zigbee devices over the internet

You are not alonne to misunderstand this. I understand this can be confiaing because it can be changed to be a Zigbee Router instead of a Zigbee Coordinator but in Zigbee Router mode it does not send any traffic from the Zigbee radio chip over over the LAN/IP network, so you can never route Zigbee Router traffic over a LAN or WAN. So in Zigbee Router mode you basically fully disconnect the Zigbee radio chip and that works completly stand-alone from the ESP32 chip that is running the serial-over-IP proxy server software.

Zigbee Router communication will only ever work over Zigbee, you can never bridge that over LAN/IP. Again, check out these community guides before buying anything: