There isn’t usually much to do on an embedded router other than use its own commands to change settings or manage packages. And if it has enough juice to run more advanced stuff it probably has bash available too.
Anyway, there’s NFS for mounting filesystems remotely. It’s not very complicated, the catch is that the same UIDs and GUIDs on the host must exist on the guest, because it doesn’t do any uid translation. On an embedded system most stuff is owned by root, meaning you’d have to use root on guest too, which may not be a great idea.
Secondly, you can’t run commands over NFS, just manipulate files and I’m not sure that’s something you really need to do a lot of on a router.