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.
sudo rm resolv.conf
sudo ln -s /run/systemd/resolve/resolv.conf resolv.conf
systemctl restart systemd-resolved