The Intel® NUC M15 Laptop Kits - LAPBC710 & LAPBC510 only support USB to Ethernet adapters with the Realtek* RTL8152 or RTL8153 chips inside.
PXE booting doesn't work on the Intel® NUC M15 Laptop Kits - LAPBC710 and/or LAPBC510.
The Intel® NUC M15 Laptop Kits - LAPBC710 & LAPBC510 only support USB to Ethernet adapters with the Realtek* RTL8152 or RTL8153 chips inside.
The USB to Ethernet adapter can be USB type C or USB type A, with a type C adapter, but it must have one of the Realtek chips listed above.
Search for an adapter using the Realtek* chip number to see what adapters are sold with those chips.