As per Cerad's comment, here is the full answer.
Below is only the part of the code related to the question & answer. These are not the full files.
Also, this is only for Symfony ^5.2 that is not using guard to authenticate the user.
/* config/packages/security.yaml */
security:
    enable_authenticator_manager: true
    firewalls:
        main:
            custom_authenticators:
                - App\Security\SecurityAuthenticator
/* src/Security/SecurityAuthenticator.php */
use Symfony\Component\Security\Http\Authenticator\AbstractLoginFormAuthenticator;
/* automatically generated with the make:auth command,
     the important part is to undestand that this is not a Guard implement 
     for the Authenticator class */
class SecurityAuthenticator extends AbstractLoginFormAuthenticator
{
  
}
/* src/Controller/RegistrationController.php */
use App\Entity\User;
use App\Form\RegistrationFormType;
use App\Security\SecurityAuthenticator;
use Symfony\Bundle\FrameworkBundle\Controller\AbstractController;
use Symfony\Component\HttpFoundation\Request;
use Symfony\Component\HttpFoundation\Response;
use Symfony\Component\Routing\Annotation\Route;
use Symfony\Component\Security\Core\Encoder\UserPasswordEncoderInterface;
use Symfony\Component\Security\Http\Authentication\UserAuthenticatorInterface;
class RegistrationController extends AbstractController
{
    /**
     * @Route("/register", name="app_register")
     */
    public function register(
        Request $request, 
        UserPasswordEncoderInterface $passwordEncoder, 
        UserAuthenticatorInterface $authenticator, 
        SecurityAuthenticator $formAuthenticator): Response
    {
      /* Automatically generated by make:registration-form, but some changes are
         needed, like the auto-wiring of the UserAuthenticatorInterface and 
         SecurityAuthenticator */
        $user = new User();
        $form = $this->createForm(RegistrationFormType::class, $user);
        $form->handleRequest($request);
        if ($form->isSubmitted() && $form->isValid()) {
            // encode the plain password
            $user->setPassword($passwordEncoder->encodePassword($user, $form->get('password')->getData()));
            $entityManager = $this->getDoctrine()->getManager();
            $entityManager->persist($user);
            $entityManager->flush();
            // substitute the previous line (redirect response) with this one.
            return $authenticator->authenticateUser(
                $user, 
                $formAuthenticator, 
                $request); 
        }
        return $this->render('registration/register.html.twig', [
            'registrationForm' => $form->createView(),
        ]);
    }
}