I would like to know why my custom post type pages do not accept paged pages?

On a normal page I can list custom post types without problems, but on a custom post type page, it seems impossible. I would like to make custom list pages to list custom posts types based on various queries.

I.e. if I would like to list all my custom post types on a page with a pagination, the URL or permalink structure would look something like this: http://www.url.com/taxonomy/document/page/2/, but I can't access that page at all, it simply redirect the additional pages (like 2, 3, 4, etc) to the root page http://www.url.com/taxonomy/document/.

I tried all kind of weird and wonderful solutions that I've found online, but nothing seems to fix it?

The reason I don't want to use a standard page with a custom template, is because it will need specific settings to set up search queries, which a normal page should not have.

This is the code snippet, and it works totally fine on a custom page template (template-list.php), but not on a custom post type page.

$entry = new ThemeOptions\PropertyListing();

$max = get_option('posts_per_page');
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;

$args = array(
        
    'post_type'         => 'property',
    'posts_per_page'    => $max,
    'paged'             => $paged,
    'tax_query'         => '',
    'meta_query'        => '',
    'post_status'       => 'publish',
    'orderby'           => '',
    'order'             => 'DESC'
);

$query = new WP_Query($args);

if ($query->have_posts()) :

    while($query->have_posts()) : $query->the_post();

        echo $entry->display($post);

    endwhile;

    $wp_query = $query;

    get_template_part('/includes/layout/pagination', '');

else:

    echo "No posts found!! <br>";

endif;

This is the custom post type on which I would like to list other post types and on which the pagination or paged pages fails.

[slug] => listing
[label] => Listing
[labels] => Array
    (
        [name] => Listings
        [singular_name] => Listing
        [menu_name] => Listings
        [all_items] => Listings
        [add_new] => Add New
        [add_new_item] => Add New Listing
        [edit] => Edit
        [edit_item] => Edit Listing
        [new_item] => New Listing
        [view] => View Listing
        [view_item] => View Listing
        [search_items] => Search Listings
        [not_found] => No Listings found
        [not_found_in_trash] => No Listings found in Trash
        [parent_item_colon] => Parent Listing
    )

[description] => Listing page is a custom page type to store and display a search listing page.
[public] => 1
[exclude_from_search] => 1
[publicly_queryable] => 1
[show_ui] => 1
[show_in_nav_menus] => 1
[show_in_menu] => 1
[show_in_admin_bar] => 1
[menu_position] => 21
[menu_icon] => dashicons-admin-page
[capability_type] => listing
[capabilities] => Array
    (
        [read] => read
        [edit_post] => edit_listing
        [edit_posts] => edit_listings
        [edit_others_posts] => edit_others_listings
        [edit_private_posts] => edit_private_listings
        [edit_published_posts] => edit_published_listings
        [publish_posts] => publish_listings
        [read_post] => read_listing
        [read_private_posts] => read_private_listings
        [delete_post] => delete_listing
        [delete_posts] => delete_listings
        [delete_others_posts] => delete_others_listings
        [delete_private_posts] => delete_private_listings
        [delete_published_posts] => delete_published_listings
    )

[map_meta_cap] => 1
[hierarchical] => 
[register_meta_box_cb] => 
[has_archive] => 
[rewrite] => Array
    (
        [slug] => listing
    )

[query_var] => 1
[can_export] => 1
[supports] => Array
    (
        [0] => title
        [1] => editor
        [2] => author
        [3] => thumbnail
        [4] => revisions
        [5] => page-attributes
    )

I'm not sure if there is anything missing to allow pagination