Similarly to what systemd-resolved does, introduce the concept of
"routing" domain, which is a domain in the search list that is used
only to decide the interface over which a query must be forwarded, but
is not used to complete unqualified host names. Routing domains are
those starting with a tilde ('~') before the actual domain name.

Domains without the initial tilde are used both for completing
unqualified names and for the routing decision.