How to convert extension attribute type string to type object?

As type string:(but I need as an object)

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
        xsi:noNamespaceSchemaLocation="urn:magento:framework:Api/etc/extension_attributes.xsd">
    <extension_attributes for="MagentoSalesApiDataOrderInterface">
        <attribute code="admin_user" type="string"/>
    </extension_attributes>
</config>

should be something like:

<attribute code="admin_user" type="pathtoobject"/>

Plugin:

<?php

declare(strict_types=1);

namespace CollinsOrderTrackingPlugin;

use MagentoSalesApiDataOrderInterface;
use MagentoSalesApiDataOrderSearchResultInterface;
use MagentoSalesApiOrderRepositoryInterface;
use CollinsOrderTrackingModelAttributesFactory;
use MagentoBackendModelAuthSession;
use CollinsOrderTrackingModelResourceModelAttributeCollectionFactory;
use CollinsOrderTrackingApiAttributesRepositoryInterface;
use MagentoFrameworkApiSearchCriteriaBuilder;
use MagentoFrameworkSessionSessionManagerInterface;

class OrderRepositoryPlugin
{
    /**
     * @var AttributesFactory
     */
    private $attributesFactory;
    /**
     * @var Session
     */
    private $session;
    /**
     * @var CollectionFactory
     */
    private $collectionFactory;
    /**
     * @var AttributesRepositoryInterface
     */
    private $attributesRepository;
    /**
     * @var SearchCriteriaBuilder
     */
    private $criteriaBuilder;

    /**
     * @param AttributesFactory $attributesFactory
     * @param Session $session
     * @param CollectionFactory $collectionFactory
     * @param AttributesRepositoryInterface $attributesRepository
     * @param SearchCriteriaBuilder $criteriaBuilder
     */
    public function __construct(
        AttributesFactory $attributesFactory,
        Session $session,
        CollectionFactory $collectionFactory,
        AttributesRepositoryInterface $attributesRepository,
        SearchCriteriaBuilder $criteriaBuilder
//        SessionManagerInterface $coreSession
    ) {
        $this->attributesFactory = $attributesFactory;
        $this->session = $session;
        $this->collectionFactory = $collectionFactory;
        $this->attributesRepository = $attributesRepository;
        $this->criteriaBuilder = $criteriaBuilder;
//        $this->sessionManager = $coreSession;
    }


    /**
     * @param OrderRepositoryInterface $subject
     * @param OrderSearchResultInterface $orderSearchResult
     * @return OrderSearchResultInterface
     */
    public function afterGetList(
        OrderRepositoryInterface $subject,
        OrderSearchResultInterface $orderSearchResult
    ): OrderSearchResultInterface {
        return $orderSearchResult;
    }

    /**
     * @param OrderRepositoryInterface $subject
     * @param OrderInterface $order
     * @return OrderInterface
     */
    public function afterGet(
        OrderRepositoryInterface $subject,
        OrderInterface $order
    ): OrderInterface {
        $key = 'collins_ordertracking_order'.$order->getEntityId();
        $adminUserId = null;
        $searchCritertia = $this->criteriaBuilder->addFilter('order_id',$order->getEntityId(),'eq');
        $sessionData = $this->session->getData($key);
        $entityId = $order->getEntityId();
        // GetList must be loaded more than once when using session.
        // Functionality below ensures that get list is ran twice but not more.
        if(!isset($sessionData)) {
            $this->session->setData($key,$entityId);
            $sessionData = $this->session->getData($key);
        }
        if($sessionData < ($entityId +2)) {
            $this->session->setData($key,intval($sessionData) +1);
            $repository = $this->attributesRepository->getList($searchCritertia->create());
            foreach ($repository->getItems() as $item) {
                $adminUserId = $item->getUserId();
            }
            if ($adminUserId != null) {
                $extensionAttributes = $order->getExtensionAttributes();
                $extensionAttributes->setAdminUser($adminUserId);
            }
        }
        return $order;
    }
}

I am trying to load the attributes in a plugin, but afterGet() loads the attributes many times. As you see, I am using session to limit the calls to 2, but that is a very bad practice. To my understanding, if I attach the object as the extension attribute oppose to using type string, then there would only be just 1 call to the database. How do I make this happen?