Redirect to webform from controller and back to custom form
What is the purpose of that redirect() method if it doesn't redirect?

You find this method in both, controller and form:
ControllerBase::redirect()
FormBase::redirect()
It creates a redirect response and you return it if a certain condition is met:
if (...) {
   return $this-&gt;redirect($route_name);
}

Example: https://drupal.stackexchange.com/a/277596/47547