I'm facing some strange issue with Perl CGI.

Nothing really strange, just real basic pitfalls , like you've never read perlintro or coping with scoping or SYNOPSIS of CGI

And then you throw mod_perl in the mix but you haven't read CGI to mod_perl Porting. mod_perl Coding guidelines

You have a lot of reading to do so you can write

#!/usr/bin/perl --
use strict; use warnings;

use CGI qw();
use CGI::Carp qw ( fatalsToBrowser );

use JSON::Parse 'parse_json';
use REST::Client;

Main( @ARGV );
exit( 0 );

sub Main {
    my $client = REST::Client->new();
    $client->setHost('http://localhost');
    
    my $q = CGI->new();
    my $adId = $q->param('adId');
    
    print $q->header, $adId;
}
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