Have a look at how this was solved in Linux 2.6.x kernel release.
https://www.howtoforge.com/creating-the-sis191-gigabit-ethernet-driver-on-linux-2.6
This web article might give a person with experience building a kernel from source with added driver modules enabled a start in the right direction at least.
A kernel module can be compiled to correctly identify the SIS191 nic and advertise it's capabilities to connected switches and routers. I myself am trying to figure out how to apply this to a newer distribution (Debian 10) with the 4.19.x kernel source so I can use this built-in nic on my old HP MediaSmart EX470 server. Keep in mind this is not a 3rd party driver as this is in the drivers/net section of the Liniux kernel source tree today.
Surely Unraid can be modified to allow a custom kernel image to be loaded by Grub and Initramfs?