You can check the email id for a specific website by using the below code.

<?php
namespace VendorModuelModel;

use MagentoCustomerApiAccountManagementInterface;
use MagentoStoreModelStoreManagerInterface;

class EmailExist {
    /**
     * @var AccountManagementInterface
     */
    protected $customerManagement;

    /**
     * @var StoreManagerInterface
     */
    protected $storeManager;

    /**
     * Data constructor.
     *
     * @param AccountManagementInterface $customerManagement
     * @param StoreManagerInterface $storeManager
     */
    public function __construct(
        AccountManagementInterface $customerManagement,
        StoreManagerInterface $storeManager
    ) {
        $this->customerManagement = $customerManagement;
        $this->storeManager = $storeManager;
    }

    /**
     *
     * @return bool
     */
    public function emailExistOrNot(): bool
    {
        $email = "testemail@email.com";
        $websiteId = (int)$this->storeManager->getWebsite()->getId();
        $isEmailNotExists = $this->customerManagement->isEmailAvailable($email, $websiteId);
        return $isEmailNotExists;
    }
}

Hope this article will help you to check customer email id’s existance.