I had an old record lying in my /etc/resolvconf.conf that injected 127.0.0.1 whenever network went up:
# /etc/resolvconf.conf
# Configuration for resolvconf(8)
# See resolvconf.conf(5) for details
resolv_conf=/etc/resolv.conf
# If you run a local name server, you should uncomment the below line and
# configure your subscribers configuration files below.
name_servers=127.0.0.1
So commented it out, then ran resolvconf -u and my issue was fixed. Currently using systemd-networkd, so dont't know for sure if this will help OP's specific case.
However, NetworkManager has a setting to make it stop updating resolv.conf:
[main]
dns=none
More information in another question at network manager: how to stop nm updating /etc/resolv.conf
Update:
The same kind of message appears when my upstream DNS servers are down/not responding. However, containing the upstream IP addresses on a round-robin basis between the server alternatives.
Update #2:
When using systemd-networkd, if you've opted to use the following DNS settings for your interface in /etc/systemd/network/<iface>.network:
[DHCP]
UseDNS=true
which is the default setting, then it will not be using your local systemd-resolved instance, but instead use the a server from DHCP. Set UseDNS=false to use your systemd-resolver. Read man systemd.network for detailed information.