You can't send a response from custom code in Drupal. You have to return it from a controller.
You can also set a response or add the cookie to an existing response in an event subscriber. In your case set the response in form submit, then Drupal does this for you in a core event subscriber:
To avoid the empty page you probably want to fill the response with content or add the cookie to a redirect response to display a different page.
To explain why not to send a response. When you find a code example for the Symfony component HttpFoundation sending a response, it isn't valid for custom code in Drupal. See the warning in this doc:
This article explains how to use the HttpFoundation features as an
independent component in any PHP application. In Symfony applications
everything is already configured and ready to use. Read the Controller
article to learn about how to use these features when creating
In addition the Drupal kernel is wrapped in stack middlewares using Stack/Builder. So sending a response can even be a security risk if you have for example installed a middleware providing security checks.