Add custom product attribute to Order API

I have added a custom product attribute via code, using InstallData.php

public function install(ModuleDataSetupInterface $setup, ModuleContextInterface $context)
    {
        $eavSetup = $this->eavSetupFactory->create(['setup' => $setup]);
        $eavSetup->addAttribute(
            MagentoCatalogModelProduct::ENTITY,
            'hts_code',
            [
                'type' => 'text',
                'backend' => '',
                'frontend' => '',
                'label' => 'HTS Code',
                'input' => 'text',
                'class' => '',
                'source' => '',
                'global' => MagentoEavModelEntityAttributeScopedAttributeInterface::SCOPE_GLOBAL,
                'visible' => true,
                'required' => false,
                'user_defined' => false,
                'default' => '',
                'searchable' => false,
                'filterable' => false,
                'comparable' => false,
                'visible_on_front' => false,
                'used_in_product_listing' => true,
                'unique' => false,
                'apply_to' => ''
            ]
        );
    }

This attribute shows in the product details page and can be set no issue. It appears in the API when fetching the product.

However, I need to add this attribute to the Order API response (http://store.test/index.php/rest/V1/orders/) but cannot figure this out at all.

I have looked up multiple examples but none of the implementations work.

So how do I go about adding this custom attribute to the Order API response, and ideally, I need to add it to the shipping_assignments.items section of the Order extension attributes