For proof, you could show a reduced version of your program that requires nothing outside of CGI::Application that exhibits the behaviour you claim.

Sample CGI::Application::Dispatch:

package Sample::Dispatch;

use strict;
use warnings;

use CGI::Application::Dispatch;
use base qw(CGI::Application::Dispatch);

sub dispatch_args {
    return {
        prefix => 'Sample',
        table  => [ q{} => { app => 'Application', rm => 'index' }, ],
    };
}

1;
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Sample CGI::Application:

package Sample::Application;

use strict;
use warnings;

use base qw(CGI::Application);

use CGI::Application::Plugin::Apache qw(:all);

sub setup {
    my ( $self, $args ) = @_;
    $self->run_modes('index' => 'index');
    $self->start_mode('index');
    return 1;
}

sub index {
    my ( $self, $args ) = @_;
    $self->header_type('none');
    $self->query->status(403);
    return q{};
}

1;
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If you set the value of $self->query->status() to 400, 404, and 500 it works as expected. Why does it not support setting any other type of status?