According to this, it seems to be a question of using the right adapter, and using /e/OS based on Android 9 didn’t seem to work.
As /e/OS on the Fairphone 3/3+ can currently be Android 9, 10 or 11 depending on how it was installed, what exactly does it say for you in Settings - About phone - Android version (tap on it) - /e/OS version?
What about the Wi-Fi hotspot feature of the phone or USB tethering?
If I connect me to my home network with the ethernet adapter on my phone it works. I can open websites even if the phone is in flightmodus…so it is not about the adapter. (But then it runs over the modem at home)
In a “chain” - “diagram”:
Internet (landline) → Modem (at home) → Switch → LAN-Cable → LAN-Adapter (to USB-C) Phone. This works fine! But that was not my concern.
There is android 10 on the phone. Android 11 has the possibility for Ethernet tethering.
USB-Tethering does not work with the Lan-Adapter. It can not be activatet.
The “Chain” should be like this.
Internet → phone → Lan-Adapter (USB-C) → Lan-Cable → Notebook
(Meanwhile I use a USB-Cable or Hotspot, But the Cable is often to short - there is often no good connection far from windows or doors and I also do not want to use wifi when I work on the notebook)
I hope they (e OS) will make soon an update to Android 11 - then the problem is solved.
One Idea I will try is an old router (if I find it :-), and I hope it works), where I can connect the phone and then share it with my devices over LAN.