I killed Cognator and got the ending slide where he's still alive.
This slide: "And so you severed the command chain right at the very core." only triggers if the player has killed Cognator without talking to him first (so talking with him and using "I'm here for revenge *Attack!*" dialogue option causes him to magically survive off-screen).
https://drive.google.com/drive/folders/1qzL9UJ51o3BDTi-Tza47GZnhRWwAQpd6?usp=sharing