How to extend TYPO3 cart product with new field in fe varient?

I am trying to extend a new field with fe varient. I have added below code:

ext_tables.sql

#
# Table structure for table 'tx_cartproducts_domain_model_product_fevariant'
#
CREATE TABLE tx_cartproducts_domain_model_product_fevariant (
    note text,
);

/myext/Configuration/TCA/Overrides/tx_cartproducts_domain_model_product_fevariant.php

<?php

defined('TYPO3_MODE') or die();

$temporaryColumns = [
    'note' => [
        'exclude' => 1,
        'label' => 'Note',
        'config' => [
            'type' => 'text',
            'eval' => 'trim',
        ],
    ],
];

\TYPO3\CMS\Core\Utility\ExtensionManagementUtility::addTCAcolumns(
    'tx_cartproducts_domain_model_product_fevariant',
    $temporaryColumns
);
\TYPO3\CMS\Core\Utility\ExtensionManagementUtility::addToAllTCAtypes(
    'tx_cartproducts_domain_model_product_fevariant',
    'note',
    '',
    'after:title'
);

Now, backend working as expected, to render value in frontend. I added model like below:

myext/Classes/Domain/Model/Product/FeVariant.php

<?php

namespace Vendor\myext\Domain\Model\Product;

class FeVariant extends \Extcode\CartProducts\Domain\Model\Product\FeVariant
{

    /**
     * note
     *
     * @var string
     */
    protected $note = '';

    /**
     * Returns note
     *
     * @return string
     */
    public function getNote()
    {
        return $this->note;
    }

    /**
     * Sets note
     *
     * @param string $note
     */
    public function setNote($note)
    {
        $this->note = $note;
    }
}

And added class mapping like below

myext/Configuration/Extbase/Persistence/Classes.php

<?php
declare(strict_types=1);

return [
    \Vendor\myext\Domain\Model\Product\FeVariant::class => [
        'tableName' => 'tx_cartproducts_domain_model_product_fevariant',
    ],
];

I also found reference here but it also not working for fe_variant.

I think you have to add some lines to your ext_localconf.php

$GLOBALS['TYPO3_CONF_VARS']['SYS']['Objects'][\Extcode\CartProducts\Domain\Model\Product\FeVariant::class] = [
    'className' => \Vendor\myext\Domain\Model\Product\FeVariant::class
];

\TYPO3\CMS\Core\Utility\GeneralUtility::makeInstance(\TYPO3\CMS\Extbase\Object\Container\Container::class)
    ->registerImplementation(
        \Extcode\CartProducts\Domain\Model\Product\FeVariant::class,
        \Vendor\myext\Domain\Model\Product\FeVariant::class
    );