Custom Post Type is not respecting assigned categories

Question

I created a custom post type "media" and added several posts with different categories assigned (Press Release, Media Resource, News Article)

On my Media archive template I use WP_Query to try and display the most recent 3 of each. Instead each section shows the most recent of ANY of them.

Also, on the "archive" page I see my categories listed but when I click on any of them they say "no posts", so my CPT is simply not playing well with the categories, any help appreciated!

function create_post_type_media()
{
    register_taxonomy_for_object_type('category', 'media'); // Register Taxonomies for Category
    register_taxonomy_for_object_type('post_tag', 'media');
    register_post_type('media', // Register Custom Post Type
        array(
        'labels' => array(
            'name' => __('Media Posts', 'html5blank'), // Rename these to suit
            'singular_name' => __('Media Post', 'html5blank'),
            'add_new' => __('Add New', 'html5blank'),
            'add_new_item' => __('Add New Media Post', 'html5blank'),
            'edit' => __('Edit', 'html5blank'),
            'edit_item' => __('Edit Media Post', 'html5blank'),
            'new_item' => __('New Media Post', 'html5blank'),
            'view' => __('View Media Post', 'html5blank'),
            'view_item' => __('View Media Post', 'html5blank'),
            'search_items' => __('Search Media Post', 'html5blank'),
            'not_found' => __('No Media Posts found', 'html5blank'),
            'not_found_in_trash' => __('No Media Posts found in Trash', 'html5blank')
        ),
        'public' => true,
        'hierarchical' => true, // Allows your posts to behave like Hierarchy Pages
        'has_archive' => true,
        'supports' => array(
            'title',
            'editor',
            'excerpt',
            'thumbnail'
        ), // Go to Dashboard Custom HTML5 Blank post for supports
        'can_export' => true, // Allows export in Tools > Export
        'taxonomies' => array(
            'post_tag',
            'category'
        )
    ));
}
add_action('init', 'create_post_type_media');

Here is one of my WP_Query for reference:

$args = array(
    'showposts' => 3,
    'post_type' => 'media',
    'category_name' => 'media-resource',
);
$query = new WP_Query( $args );
if ($query->have_posts()) : ?>

Answer 1

I'm going to quote this answer https://wordpress.stackexchange.com/a/242254/91219

Order really shouldn't really matter but it's good practice to register things in a hierarchical structure.

    register_post_type( $cpt, $args );
    register_taxonomy( $catname, $cpt );