Copy t/v1.t to t/v2.t and add two lines testing the Access-Control-Allow-Origin header and the lack of it.

subtest v1_greeting => sub {
    my $res  = $test->request( GET '/api/v1/greeting' );
    ...
    is $res->header('Access-Control-Allow-Origin'), undef;
}
subtest v2_greeting => sub {
    my $res  = $test->request( GET '/api/v2/greeting' );
    ...
    is $res->header('Access-Control-Allow-Origin'), '*';
}
perl Makefile.PL
make
make test