Correctly order the hierarchy of custom taxonomy when displaying terms

If you want to show a term and all its parents/ancestors, you can do the following:

function display_term_parents( \WP_Term $starting_term ) {
    $terms = [];
    $term = $starting_term;
    while ( !is_wp_error( $term ) ) {
        $terms[] = $term->name;
        $term = get_term( $term->parent, 'kernal_category' );
    }
    $terms = array_reverse( $terms );
    echo implode(' > ', $terms );
}

Where $starting_term is the term you want to show the ancestors/parents for.

This can be done for each term ( or just the first term ) that a post has, assuming that you’ve only checked the term you want, but not all of its parents too