Do the inverse remove the r8168 package and reboot and tell us if it works ?
The hardware problem comes from Realtek firmware. Some hardware takes only r8168 likes my old Linksys which is wrongly detected as r8169 by default but some others r8168 works with the r8169 driver…
In your case it seems to work with the r8169 here Solved -- Help with Realtek module r8169
check your services systemctl if it’s enable or not…