How do I redirect after saving the user account with $user->save()?
I suppose you want to remain on your site when redirecting.
I don't recommend hardcoded URL's anywhere else but in route.yml files.
Call the right service and don't forget to use dependency injection in your services and don't use a trait or directly call it from the container.

  private function redirect(string $route) {
    $path = $this-&gt;container-&gt;get('url_generator')-&gt;getPathFromRoute($route);
    return new RedirectResponse($path);
  }