[BUG] Uploading a product with this library fails and creates a broken product

Related to https://github.com/woocommerce/woocommerce/issues/40832

Describe the bug

When a new product is added via the Automattic\WooCommerce\Client library, the WordPress encounters a fatal error, and the library receives an invalid response:

Fatal error: Uncaught Automattic\WooCommerce\HttpClient\HttpClientException: Error: <p>W witrynie wystąpił błąd krytyczny.</p><p><a href="https://wordpress.org/documentation/article/faq-troubleshooting/">Dowiedz się więcej o rozwiązywaniu problemów z WordPressem.</a></p> [internal_server_error] in C:\Users\oskar\vendor\automattic\woocommerce\src\WooCommerce\HttpClient\HttpClient.php:383 Stack trace: #0 C:\Users\oskar\vendor\automattic\woocommerce\src\WooCommerce\HttpClient\HttpClient.php(419): Automattic\WooCommerce\HttpClient\HttpClient->lookForErrors(Object(stdClass)) #1 C:\Users\oskar\vendor\automattic\woocommerce\src\WooCommerce\HttpClient\HttpClient.php(455): Automattic\WooCommerce\HttpClient\HttpClient->processResponse() #2 C:\Users\oskar\vendor\automattic\woocommerce\src\WooCommerce\Client.php(56): Automattic\WooCommerce\HttpClient\HttpClient->request('products', 'POST', Array) #3 C:\xampp\htdocs\konrad\wp-content\plugins\product-importer-plugin\insert-test.php(27): Automattic\WooCommerce\Client->post('products', Array) #4 {main} thrown in C:\Users\oskar\vendor\automattic\woocommerce\src\WooCommerce\HttpClient\HttpClient.php on line 383

The API credentials are correct, otherwise, an error would be different.
The screenshot clearly shows that a product is broken:


Below it is an example of a working product:

Expected behavior

A product appears on the store page with the provided parameters

Actual behavior

The WooCommerce API returns an invalid response and causes a fatal error, and a broken product appears in the admin menu, but not the product listing. Additionally, the displayed product count is higher by 1 than actual count of working products

Steps to reproduce

Create a PHP script and visit it with the browser. Replace the autoload and API configs:

<?php
	//Include the WooCommerce API Client in Your PHP File
	require_once '\vendor\autoload.php'; // Replace with the path to your vendor/autoload.php
	// Include PHPExcel
	use PhpOffice\PhpSpreadsheet\IOFactory;
	use Automattic\WooCommerce\Client;
	// WooCommerce API credentials
	$api_url = 'http://example.com/'; // Your store's URL
	$api_key = 'ck_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'; // Replace with your API key
	$api_secret = 'cs_xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx'; // Replace with your API secret

	// Initialize the WooCommerce API client with your credentials
	$woocommerce = new Automattic\WooCommerce\Client($api_url, $api_key, $api_secret, ['version' => 'wc/v3']);
	
	// Define WooCommerce product data
	$product_data = [
		'name' => 'DebugTestProduct', // Product name without SKU
		'type' => 'simple',
		'regular_price' => '123',
		'description' => '',
		'short_description' => '',
		'stock_quantity' => 12,
		'sku' => 'PR123', // Product SKU (product number)
	];

	// Add the product to WooCommerce
	$new_product = $woocommerce->post('products', $product_data);

	// Check for errors or handle success as needed
	if (is_wp_error($new_product)) {
		echo 'Error importing product: ' . $new_product->get_error_message() . '<br>';
	} else {
		echo 'Product imported successfully: ' . $new_product->name . '<br>';
	}
?>

Reproduce the POST to products using the provided PHP script, then trace src/WooCommerce/Client.php and src/WooCommerce/HttpClient/HttpClient.php around the reported lines 383, 419, and 455. Determine whether the client or the server response accounts for the fatal error; done means the product is created successfully without an invalid response or broken listing entry.