It was sentient but under Batman's command. Alexander Luthor only made it realize that it could be so much more if it refused its creator and followed its own objectives.
Announcing that "the Great Disaster has come to me," the Eye directs Karate Kid to Blüdhaven. Soon after, it reactivates its offensive protocols and assimilates the hangar it is being held in, turning the people within the hangar into new OMAC cyborgs, and itself travels to the ruins of Blüdhaven and assimilates its infrastructure and the people within it, using the Atomic Knights and Firestorm as power sources
You seem to be going in circles and are now back to saying it is only a surveillance system. Who are you trying to convince? Me or You?
"It was then revealed that Brother Eye was wrested away from Batman by Alexander Luthor, Jr. and became an important part of Alex Luthor's plan to bring back the Multiverse. Luthor granted the satellite sentience
, allowing it to evolve into a brain capable of directing the energies of the dimensional "tuning fork"."
Lol, taking over passive infrastructure like a freaking hangar, and a primitive city, means jack shit to Doom. Brother Eye couldn't even assimilate a single Doombot, forget someone who easily has the technological and magical prowess to absolutely destroy the Brother Eye satellite, pr take IT over.
I never said Batman's version was anything but a simple surveillance system, that's all it was designed to do. It never did anything else until it gained sentience. Unfortunately, Batman's version is not sentient.