The save/restore DNS functionality always perform its job, even though
the DNS is not static, aka set by DHCP. That may lead to confusion to
users. Since DHCP settings was changed to static settings, even though
the namesers set are the same.
To fix this, ctrld should save/restore only there's actual static DNS
set. For DHCP, thing should work as-is like we are doing.
On some routers, change to network may trigger re-rendering
/etc/resolv.conf file, causing requests from router itself stop using
ctrld.
Fixing this by watching changes to /etc/resolv.conf, then revert them.