Unable to save custom Customer Attributes in Magento 2.4.5-p1 Order Placement Observer

I’ve created a new custom attribute as below:

namespace VendorModuleSetup;
use MagentoEavSetupEavSetup;
use MagentoEavSetupEavSetupFactory;
use MagentoFrameworkSetupInstallDataInterface;
use MagentoFrameworkSetupModuleContextInterface;
use MagentoFrameworkSetupModuleDataSetupInterface;
use MagentoCustomerModelCustomer;
use MagentoEavModelConfig;

class InstallData implements InstallDataInterface
{
private $eavSetupFactory;
private $eavConfig;

public function __construct(EavSetupFactory $eavSetupFactory, Config $eavConfig)
{
$this->eavSetupFactory = $eavSetupFactory;
$this->eavConfig = $eavConfig;
}

public function install(ModuleDataSetupInterface $setup, ModuleContextInterface $context)
{
    $eavSetup = $this->eavSetupFactory->create(['setup' => $setup]);

    $attributes = [
        'id_number' => [
            'type' => 'varchar',
            'label' => 'ID Number',
            'input' => 'text',
            'required' => false,
            'user_defined' => true,
            'visible' => true,
            'position' => 120,
            'system' => false,
        ],
    ];

    foreach ($attributes as $attributeCode => $attributeDetails) {
        $eavSetup->addAttribute(Customer::ENTITY, $attributeCode, $attributeDetails);

        $attribute = $this->eavConfig->getAttribute(Customer::ENTITY, $attributeCode);
        $attribute->setData(
            'used_in_forms',
            ['adminhtml_customer', 'customer_account_create', 'customer_account_edit']
        );
        $attribute->save();
    }
}

}

I’ve tried several solutions to save any data in this field using order success observer, but in vain. No errors and customer save works successfully. e.g.:

if ($isCustomerLoggedIn) {
//$customer = $this->customerRepository->getById($customerId);
$customer = $this->customerFactory->create()->load($customerId);

        // Set custom attributes
        $customerData->setCustomAttribute('id_number', $this->customerSession->getData('id_number'));

        $customer->setDob($this->customerSession->getData('dob'));
        // Save custom data in customer entity
        $customerDataModel = $customer->getDataModel();
        $customerDataModel->setCustomAttribute('id_number', '12345');

        try {
            $customer->updateData($customerDataModel);
            //$this->customerRepository->save($customer);
            $customer->save();
            $this->messageManager->addSuccessMessage(__('Customer data has been saved.'));
        } catch (Exception $e) {
            $this->messageManager->addErrorMessage(__('Error saving customer data %1', $e->getMessage()));
        }

Any help? Please provide a working code for Magento 2.4 so I can try it again. Note that even setDob seems not working as well.

Thanks in advance!