tests: net: getaddrinfo: Fix test to check the query is sent

As the getaddrinfo() test is suppose to be self contained, then
we will need to install handler for the sent DNS query. After we
receive the query in process_dns() thread, we verify that the
query was sent properly. We do not return DNS reply back to
the caller in this case as we do not want to create DNS server
just for this simple test application. This can be changed later
if we get DNS server functionality in Zephyr network stack.

Fixes #15193

Signed-off-by: Jukka Rissanen <jukka.rissanen@linux.intel.com>