Custom Sort Order for Custom Post Type Taxonomy

Use usort with a custom callback, like this:

function compare_term_order_numbers( \WP_Term $a, \WP_Term $b ) : int {
    $order_number_a = get_field( 'order_number', $a );
    $order_number_b = get_field( 'order_number', $b );
    return strcmp( $order_number_a, $order_number_b );
}

usort($terms, 'compare_terms' );

Note that this assumes get_field returns a plain string, not an object, that each term has the order_number set and it isn’t empty, and that $terms is an array of terms, not an error object or false/null.

More information at: https://www.php.net/manual/en/function.usort.php