I doubt that there is currently an approved one from OSMC perspective. But to be honest Linux support for USB Ethernet adapters is quite well established.
I guess most of them will work, unless they are brand new and need a driver that is only available for 4.x Kernel.
Well based on the webpage it uses RTL8153 chipset which should be supported by the r8152.ko module which is part of OSMC on the vero4k. So unless there is a configuration option missing for the 8153 it should work
https://cateee.net/lkddb/web-lkddb/USB_RTL8152.html