How to configure a custom POST api to accept a request with Content-Type as "application/x-www-form-urlencoded" in the header?

I created a controller in a custom module that accepts a POST request.
I have a setup such that I get a POST request from a third-party application server to this API. But the POST request has a Content-Type: "application/x-www-form-urlencoded" in the header.
And because of this I get the following error in the recent log messages:

Symfony\Component\HttpKernel\Exception\UnsupportedMediaTypeHttpException: No route found that matches "Content-Type: application/x-www-form-urlencoded" in Drupal\Core\Routing\ContentTypeHeaderMatcher->filter() (line 49 of /var/www/html/web/core/lib/Drupal/Core/Routing/ContentTypeHeaderMatcher.php).```

When I test the API using postman:

1. if I use the Content-Type: "application/json" in the header, the code inside the API is executed, and I get the correct response.
2. if I use the Content-Type: "application/x-www-form-urlencoded", I get the same error.

I cannot configure the third party application server to change the Content-Type. So the only option for me is to configure the API to accept the POST request with the Content-Type: "application/x-www-form-urlencoded". How can I do that?

Edited: My class extends the class ResourceBase. Route definition of the controller. Also I am using drupal 8.

 * @RestResource(
 *   id = "test_abc_callback",
 *   label = @Translation("Custom API for Test"),
 *   uri_paths = {
 *     "create" = "/api/v1/test_callback",
 *   }
 * )

This is not a custom controller. For the original question you would need to define the method POST in a custom route. See https://www.drupal.org/docs/drupal-apis/routing-system/structure-of-routes

But you don't necessarily need a custom controller. You can add serializers to REST API for formats already defined in the Symfony request object:

Request::initializeFormats

protected static function initializeFormats()
{
    static::$formats = [
        'html' => ['text/html', 'application/xhtml+xml'],
        'txt' => ['text/plain'],
        'js' => ['application/javascript', 'application/x-javascript', 'text/javascript'],
        'css' => ['text/css'],
        'json' => ['application/json', 'application/x-json'],
        'jsonld' => ['application/ld+json'],
        'xml' => ['text/xml', 'application/xml', 'application/x-xml'],
        'rdf' => ['application/rdf+xml'],
        'atom' => ['application/atom+xml'],
        'rss' => ['application/rss+xml'],
        'form' => ['application/x-www-form-urlencoded'],
    ];
}

See https://www.drupal.org/docs/drupal-apis/serialization-api/adding-new-formats and How can I POST x-www-form-urlencoded data from REST API plugin?