when you did try different boards - did you also try all of the !three! usb-ports on every board?
specially the single one on the other side of the eth0-port? Because in you first dmesg the USB-Ethernet adapter was recognized as eth1 and then renamed.
And this renamed name wouldnt go in every situation automatically up for ifconfig.
So check the other usb-ports and when you will see enx00e04c680046 in dmesg get him up with
ifconfig enx00e04c680046 up
and then he would be displayed in
when the port is down (not automatically up or no cable/link connected the interface is in down state) then it wouldnt displayed by
The part after enx is the MAC-address of your USB3.0 Ethernet-adapter.
I got this model running on my devices without special power supply and from my personal view there is no driver problem with armbian and this device.
388 [ 5.571663] usbcore: registered new interface driver r8152
413 [ 5.906764] r8152 4-1:1.0 eth1: v1.09.9
414 [ 6.188868] EXT4-fs (zram0): mounted filesystem without journal. Opts: discard
415 [ 6.552250] r8152 4-1:1.0 enx00e04c680046: renamed from eth1
but not in the second one.
@cam2019 did you use another USB-Port? Maybe that has to be enabled in armbian-config -> system -> hardware ?