WordPress – Sort taxonomies by surname rather than name

I added this code to functions.php

// Breaks the fullname into first and last on-save and adds as metadata
add_action( 'created_autorzy', 'save_autorzy_meta', 10, 2 );

function save_autorzy_meta( $term_id, $tt_id ){
    $taxonomy = 'autorzy';
    $term = get_term($term_id, $taxonomy);

    if ( isset($term['name']) ){
        $name = explode(" ", $term['name']);
        $firstName = $name[0] ?? "";
        $lastName = $name[1] ?? "";

        update_term_meta( $term_id, 'firstName', $firstName );
        update_term_meta( $term_id, 'lastName', $lastName );
    }
}

Then in the php template I added

<?php
      $taxonomy = 'autorzy'; // <== Here define your custom taxonomy
        $sorted   = array(); // Initializing

        // Get all terms alphabetically sorted
        $terms = get_terms( array(
            'taxonomy'   => $taxonomy,
            'hide_empty' => false,
            'orderby'    => 'name'
        ) );

        // Add a query for our taxonomy with a custom metaquery
        $result = new WP_Query( array(
            'tax_query' => array(
                array(
                    'taxonomy' => $taxonomy,
                    'hide_empty' => false,
                ),
            ),
            'meta_query' => array(
                'relation' => 'AND',
                'last_names' => array(
                    'key' => 'lastName',
                    'compare' => 'EXISTS',
                ),
                'first_names' => array(
                    'key' => 'firstName',
                    'compare' => 'EXISTS',
                ), 
            ),
            'orderby' => 'meta_value_num',
            'meta_key' => 'lastName',
            'order' => 'ASC',
        ) );


        // Loop through the array of WP_Term Objects
        foreach( $terms as $term ) {
            $term_name    = $term->name;
            $image = get_field('obrazek_wyrozniajacy', $term);
            $term_link    = get_term_link( $term, $taxonomy );
            $first_letter = strtoupper($term_name[0]);
            
            // Group terms by their first starting letter
            if( ! empty($term_link) ) {
                $sorted[$first_letter][] = '<li><a href="'.$term_link.'">' .'<img src="'.$image['url'].'" />'.$term_name.'</a></li>';
            } else {
                $sorted[$first_letter][] = '<li>'.$term_name.'</li>';
            }
        }

        // Loop through grouped terms by letter to display them by letter
        foreach( $sorted as $letter => $values ) {
            echo '<div class="tax-by-letter" id="tax-letter-'.$letter.'">
            <h3 class="tax-letter-'.$letter.'">'.$letter.'</h3>
            <ul class="nav">' . implode('', $values) . '</ul>
            </div>';
        }


      ?>

Unfortunately, nothing has changed and authors are still sorted by name.