Adding count also to parent categories

You could add this to your code:

function custom_add_count_on_archive_title( $title ) {
    $term = get_queried_object();
    $term_id = get_queried_object()->term_id;
    if( $term instanceof WP_Term && 'category' === $term->taxonomy ) {
        
        $children_terms = get_terms(array(
            'taxonomy' => 'category',
            'child_of' => $term_id,
        ));
        
        $total_count = 0;
        
        if (!empty($children_terms) && !is_wp_error($children_terms)) {
            foreach ($children_terms as $child_term) {
                $total_count += $child_term->count;
            }
        }
    
        $title .= ' <span>'.$total_count.'</span>';
    }
    return $title;
}
add_filter( 'get_the_archive_title', 'custom_add_count_on_archive_title', 10, 1 );

Have not tested it but theoretically it should work. What it does is gets the children of the current term. Iterates through them and totals the count of them.