How do I name the {custom} Publish Kind identify and everlasting hyperlink to my php file?

I’ve added a Customized Publish Kind to my web site, however I can not work out what to kind once I need to add the identify and hyperlink to my template file as a class. How do I name up Publish Kind identify and handle from my php file?

Publish Kind House Web page: https://wisekitten.com/cat-breeds/

Publish Kind Content material Web page: https://wisekitten.com/cat-breeds/york-chocolate/

The codes are as follows;

perform post_type_cat_breeds() {
    $labels = array(
        'identify' => 'Cat Breeds',
        'singular_name' => 'Cat Breed'
    );
    $args = array(
        'labels' => $labels,
        'has_archive' => true,
        'public' => true,
        'hierarchical' => false,
        'helps' => array(
            'title',
            'editor',
            'excerpt',
            'writer',
            'custom-fields',
            'thumbnail',
            'feedback',
        ),
        'rewrite' => array( 'slug' => 'cat-breeds' ),
        'show_in_rest' => true,
    );
    register_post_type( 'cat_breeds', $args );
}
add_action( 'init', 'post_type_cat_breeds' );