Send custom select shipping method from cart to checkout page - wordpress

Question

I have this code for adding custom select field for method shipping
// Add custom fields to a specific selected shipping method
add_action( 'woocommerce_after_shipping_rate', 'carrier_custom_fields', 20, 2 );
function carrier_custom_fields( $method, $index ) {
if( (is_checkout() === 'false') OR (is_cart() === 'false') ) { return; } // Only on checkout page
$chosen_methods = WC()->session->get( 'chosen_shipping_methods' );
$chosen_shipping = $chosen_methods[0];
if( $method->id != 'flat_rate:3' ) return;
if ($chosen_shipping == 'flat_rate:3') {
echo '<div class="tk"><div class="td_title">Выберите транспортную компанию:</div>';
woocommerce_form_field( 'shipping_tk', array(
'type' => 'select',
'options' => array(
'delovye-linii' => __('Деловые линии', 'woocommerce' ),
'bajkal-servis' => __('Байкал Сервис', 'woocommerce' ),
'trans-vektor' => __('Транс Вектор', 'woocommerce' ),
'mejdzher-ehkspress' => __('Мейджер экспресс', 'woocommerce' ),
'cdek' => __('CDEK', 'woocommerce' ),
'transportnye-tekhnologii' => __('Транспортные технологии', 'woocommerce' ),
'zheldorehkspediciya' => __('Желдорэкспедиция', 'woocommerce' ),
'zheldoralyans' => __('Желдоральянс', 'woocommerce' ),
'kashalot' => __('Кашалот', 'woocommerce' ),
'dpd' => __('ДПД', 'woocommerce' ),
'magic-trans' => __('Мейджик Транс', 'woocommerce' ),
'severyug' => __('Север-Юг', 'woocommerce' ),
'skif' => __('Скиф Карго', 'woocommerce' ),
'vozovoz' => __('Возовоз', 'woocommerce' ),
'express-avto' => __('Экспресс Авто', 'woocommerce' ),
'nord-tranzit' => __('Норд Транзит', 'woocommerce' )
),
'default' => 'delovye-linii',
'class' => array('shipping_tk'),
'input_class' => array('shipping_tk'),
'required' => false,
), WC()->checkout->get_value( 'shipping_tk' ));
echo '</div>';
}
}
// Save custom fields to order meta data
add_action( 'woocommerce_checkout_update_order_meta', 'carrier_update_order_meta', 30, 1 );
function carrier_update_order_meta( $order_id ) {
$name_tk = array(
'delovye-linii' => 'Деловые Линии ТК',
'bajkal-servis' => 'Байкал-Сервис ТК',
'trans-vektor' => 'Вектор Экспресс (Транс Вектор) ТК',
'mejdzher-ehkspress' => 'МейджерЭкспресс ТК',
'cdek' => 'СДЭК Глобал ТК',
'transportnye-tekhnologii' => 'Транспортные Технологии ТК',
'zheldorehkspediciya' => 'ЖелдорЭкспедиция ТК',
'zheldoralyans' => 'Азбука логистики (ЖелДорАльянс) ТК',
'kashalot' => 'Кашалот (КИТ) ТК',
'dpd' => 'ДПД-Рус ТК',
'magic-trans' => 'Мейджик Транс ТК',
'severyug' => 'Север-Юг ТК',
'skif' => 'Скиф Карго ТК',
'vozovoz' => 'ТК Возовоз',
'express-avto' => 'Экспресс Авто',
'nord-tranzit' => 'Норд Транзит ТК'
);
if( isset( $_POST['shipping_tk'] )) {
$key_tk = $_POST['shipping_tk'];
update_post_meta( $order_id, '_shipping_tk', sanitize_text_field( $name_tk[$key_tk] ) ); }
if( isset( $_POST['shipping_tk2'] )) {
$key_tk = $_POST['shipping_tk'];
update_post_meta( $order_id, '_shipping_tk', sanitize_text_field( $name_tk[$key_tk] ) ); }
if( isset( $_POST['order_track'] )) {
$key_tk = $_POST['order_track'];
update_post_meta( $order_id, '_order_track', sanitize_text_field( $name_tk[$key_tk] ) ); }
}
enter image description here
But when go in checkout field my selected option in custom field is default. For example, in cart i select 3 option in select, but in checkout it is not saved.
code in cart-shipping.php file
<ul id="shipping_method" class="woocommerce-shipping-methods">
<?php foreach ( $available_methods as $method ) : ?>
<li>
<?php
if ( 1 < count( $available_methods ) ) {
printf( '<input type="radio" name="shipping_method[%1$d]" data-index="%1$d" id="shipping_method_%1$d_%2$s" value="%3$s" class="shipping_method" %4$s />', $index, esc_attr( sanitize_title( $method->id ) ), esc_attr( $method->id ), checked( $method->id, $chosen_method, false ) ); // WPCS: XSS ok.
} else {
printf( '<input type="hidden" name="shipping_method[%1$d]" data-index="%1$d" id="shipping_method_%1$d_%2$s" value="%3$s" class="shipping_method" />', $index, esc_attr( sanitize_title( $method->id ) ), esc_attr( $method->id ) ); // WPCS: XSS ok.
}
if ( $method->id == 'flat_rate:3' OR $method->id == 'flat_rate:7' ) {
printf( '<label for="shipping_method_%1$s_%2$s">%3$s</label>', $index, esc_attr( sanitize_title( $method->id ) ), wc_cart_totals_shipping_method_label( $method ) );
// WPCS: XSS ok.
} else {
printf( '<label for="shipping_method_%1$s_%2$s">%3$s</label>', $index, esc_attr( sanitize_title( $method->id ) ), wc_cart_totals_shipping_method_label( $method ) ); // WPCS: XSS ok.
}
do_action( 'woocommerce_after_shipping_rate', $method, $index );
?>
</li>
<?php endforeach; ?>
</ul>
I want to save selected option and send it to checkout page