Hi @hrlil, and welcome!
I’ve only read this very quickly, but here
…it clearly states that the Realtek RTL8111/8168/8411 PCI Express Gigabit Ethernet
has no driver. But luckily there is a driver for 8168
in the AUR:
$ pamac search 8168
r8168-dkms 8.051.02-2 AUR
A kernel module for Realtek 8168 network cards (DKMS version)
[...]
So it can be quite easily installed using:
pamac build r8168-dkms
I recommend the -dkms
version ass that will survive kernel upgrades of the same major version,
Hope this helps!