Indifference is a betrayal too. What did Mab say about hate and love? She thinks logic is the opposite but it actually is indifference / apathy.
However, the Archive feels none of that, or shouldn't and retain her mental health. As Luccio says
in Small Favor. "As a defense, the Archive began to distance themselves from other human beings,
emotionally.
She goes on to say; "Archive keeps its host emotionally remote for a reason---because otherwise the
passions and prejudices and hatreds and jealousies of thousands of lifetimes have potential to distil themselves into a single being."
So it seems that Ivy has grown up, she has become "The Archive." Any pain she may have felt emotionally by Harry's suicide or Kincaid's assistance, she has removed herself except for on final request/order to Kincaid, make it a chest shot [possible survival] instead of a head shot, [most likely certain death.] Ivy knows both were her only friends, but the Archive knows she cannot have any friends.