Your variable is undefined because there wasn't an answer to the specific question you asked

From the Net::DNS::Resolver documentation:

Returns a "Net::DNS::Packet" object, or "undef" if no answers were found. If you need to examine the response packet whether it contains any answers or not, use the send() method instead.

This amended code uses send() instead:

use strict;
use warnings;
use Net::DNS;

my $domain = $ARGV[0];

#192.48.79.30 is j.gtld-servers.net

my $res = Net::DNS::Resolver->new(
        nameservers => [qw(192.48.79.30)],
        recurse     => 1,
        debug       => 1,
  );

my $packet = $res->send("$domain", 'NS');

my @authority = $packet->authority;

foreach my $rr (@authority) {
        print $rr->string, "\n";
}
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#!/usr/local/bin/perl

use strict;
use warnings;
use Net::DNS;
use Net::DNS::Resolver::Recurse;

check_domain(@ARGV);
exit;

sub check_domain {
    my ( $domain, $class ) = @_;
    $class ||= "IN";

    print "-" x 70, "\n";
    print "$domain (class $class)\n";
    print "\n";

    my $res = Net::DNS::Resolver::Recurse->new(
        timeout => 120,
        recurse => 1,
        debug   => 1,
    );
    $res->defnames(0);
    $res->retry(2);
    

    my $nspack = $res->query( $domain, "NS", $class );

    unless ( defined($nspack) ) {
        warn "Couldn't find nameservers for $domain: ", $res->errorstr
+ing, "\n";
        return;
    }
    print "nameservers (will request zone from first available):\n";

    my $ns;
    foreach $ns ( grep { $_->type eq "NS" } $nspack->answer ) {
        print "\t", $ns->nsdname, "\n";
    }
    print "\n";

    $res->recursion_callback(
        sub {
            my $packet = shift;

            $_->print for $packet->additional;
            printf( ";; Received %d bytes from %s\n\n",
                $packet->answersize, $packet->answerfrom );
        }
    );
    $res->query_dorecursion(@ARGV);
}
exit;
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