nslookup www.domain.com
Server: 127.0.0.53
Address: 127.0.0.53#53
The network manager tool does not pass per-interface DNS configuration to systemd-resolved. Recent versions of NetworkManager, for example, would do this automatically if /etc/resolv.conf is a symlink pointing inside /run/systemd/resolve or to /usr/lib/systemd/resolv.conf. Alternatively, recent versions of systemd-resolved try to be compatible with the historical resolvconf interface by installing a resolvconf binary that talks to systemd-resolved.
cd /etc
sudo rm resolv.conf
sudo ln -s /run/systemd/resolve/resolv.conf resolv.conf
systemctl restart systemd-resolved