Looks like you can get a PoE to USB-C adapter for $35:
Revotech PoE to Type-C Adapter Converter, Convert POE to Output 5V/2.4A USB C with Ethernet, IEEE802.3af with 10/100Mbps , Wired Broadband and PD Charging for Smart Phone/Tablet, Plug and Play (P2C5V) https://a.co/d/7320MNa
Wonder how complex it is to access the network this way. If you have to modify the USB implementation you may as well skip the adapter and add an RJ45 + internal PoE chip…
TI has PoE chips for around $4, but I don’t know enough about electrical engineering to figure out how to swap that into this design.
https://www.ti.com/product/TPS23861