Ethernet-over-usb not working with usb-c to usb-c cable, working with adapter
I think the problem is that your USB-C to USB-C cable is in fact power only.
The setup you have should work when you connect it directly, but you write the USB part of System Report gives no indication that anything at all is plugged in. If you have used a charger cable that has no data lines, this is what would happen.
Try with a different USB-C to USB-C cable and it should hopefully work.
UPDATE: Based on your comments, the problem seems to be that the device itself doesn't actually support USB-C fully. You'll need to configure the Linux kernel with the CONFIG_TYPEC option in make menuconfig in order to have support for USB-C build.