Ubuntu broke DNS resolution by creating a fancy wrapper around it. As a consequence, you’ll see a whole lot of noise in /etc/resolv.conf and not your actual name server. The noise includes information on “not making changes” in the file.
To see your WHAT THE ACTUAL name servers, do this:
resolvectl status
or
systemd-resolve --status
It does the same thing.
To update your ACTUAL name servers, do this:
resolvectl dns eth0 1.1.1.1 8.8.4.4
To persist the actual change, read more and more and more internet help guides and get frustrated.
By some accounts you have to uncomment DNS= in /etc/systemd/resolved.conf but hoorah it doesn’t work and life is short.
Either way, after experimenting with the file resolved.conf you’ll have to restart the service.
systemctl restart systemd-resolved