StreamedResponse is not working with BrowserKit after Symfony is upgraded to 6.1

[fabmlk]

API Platform version(s) affected: ^3.0

Description
This is in direct relation to https://github.com/symfony/symfony/issues/46445 with Symfony ^6.1.

The proposed temporary fix https://github.com/symfony/symfony/issues/46445#issuecomment-1655564471 does not work well when using ApiPlatform\Symfony\Bundle\Test\Client as we need to call an internal method:

// $client::getResponse() marked @internal
$content = $client->getResponse()->getBrowserKitResponse()->getContent();