My kernel is: 5.13.6-artix1-1
The output of dmesg is:
$ sudo dmesg | grep r8169
[ 3.114305] r8169 0000:04:00.2: can't disable ASPM; OS doesn't have ASPM control
[ 3.118021] libphy: r8169: probed
[ 3.118304] r8169 0000:04:00.2 eth0: RTL8411, 78:24:af:72:60:59, XID 488, IRQ 34
[ 3.118310] r8169 0000:04:00.2 eth0: jumbo features [frames: 9194 bytes, tx checksumming: ko]
[ 4.636385] RTL8211E Gigabit Ethernet r8169-0-402:00: attached PHY driver (mii_bus:phy_addr=r8169-0-402:00, irq=MAC)
[ 4.848435] r8169 0000:04:00.2 eth0: Link is Down
where eth0 appears as "Link is Down"
I've tried to use dhcpcd but it doesn't help.
You could try setting it 'up' manually and see if that works, or if you get some error messages that might give more of a clue:
$ ip link show
# ip link set enpXXXX up
There is troubleshooting info for network connections on the Arch wiki that might help (saying vaguely) ... :D