How can I get the current user into my entity class?

First, to simplify things and help you get going, I'll create an interface that this user tracking entity needs to follow:

interface UserTracking
{
    public function addedBy(UserInterface $user);
    public function updatedby(UserInterface $user);
    public function getAddedBy(): ?UserInterface;
    public function getUpdatedBy(): ?UserInterface;
}

Then you can create a Doctrine event listener and inject the Securitycomponent into it:

class UserDataListener 
{
    protected $security;

    public function __construct(Security $security)
    {
        $this->security = $security;
    }

    public function prePersist(LifecycleEventArgs $event): void
    {
        $entity =  $event->getObject();
        $user   = $this->security->getUser();

        // only do stuff if $entity cares about user data and we have a logged in user
        if ( ! $entity instanceof UserTracking || null === $user ) {
            return;
        }

        $this->setUserData($entity, $user);
    }

    private function preUpdate(LifecycleEventArgs $event) {
        $this->prePersist($event);
    } 

    private function setUserData(UserTracking $entity, UserInterface $user)
    {

        if (null === $entity->getAddedBy()) {
            $entity->addedBy($user);
        }

        $entity->updatedBy($user);
    }
}    

You need to mark the listener appropriately to fire on prePersistand preUpdate:

services:
  user_data_listener:
    class: App\Infrastructure\Doctrine\Listener\UserDataListener
    tags:
      - { name: doctrine.event_listener, event: prePersist }
      - { name: doctrine.event_listener, event: preUpdate }

While the above should work, I believe that using Doctrine events this way is generally not a good idea , since you are coupling your domain logic with Doctrine and hiding your changes under a layer of magic, which is not useful for other development Personnel may not be immediately apparent. use your application.

I take it createdByas a constructor parameter and set updateByit explicitly if needed . It's only one line of code at a time, but you get clarity, expressiveness, and a simpler system with fewer moving parts.

class FooEntity
{    
    private $addedBy;
    private $updatedBy;
    public function __construct(UserInterface $user)
    {
        $this->addedBy = $user;
    }

    public function updatedBy(UserInterface $user)
    {
        $this->updatedBy = $user;
    }
}

This gives a better representation of what's going on with the domain, and future coders in your app don't have to dig through which extensions you might have installed and enabled or what events are being fired.