I found out that this is related to https://bugs.launchpad.net/ubuntu/+source/systemd/+bug/1624320 Network manager *does* add the DNS servers, but they are never used. The workaround in comment #57 fixes the problem.
I found out that this is related to https:/ /bugs.launchpad .net/ubuntu/ +source/ systemd/ +bug/1624320
Network manager *does* add the DNS servers, but they are never used. The workaround in comment #57 fixes the problem.