How to reference an instantiated game object with code? Or, something else?

Unity Engine
,
2

First, for future posts best to post your code in code tags: Using code tags properly

But you want to the enemy to grab a reference to the player, and vice versa, within the collision callback.

Something like this as a rough example:

private void OnCollisionEnter2D(Collision2D collision)
{
    if (collision.gameObject.TryGetComponent(out Player player))
    {
        player.TakeDamage();
    }
}

Don’t even need tags.

A lot of Unity for certain types of gameplay is checking for particular components via collisions or triggers and reacting to their presence.