Departments are people. By "guy in a room" I was meaning that there isn't an AI monitoring every widget on the ship. Harry is monitoring the functions of the ship which are all mostly staffed by people who input towards the data Harry collects on the bridge. Although it's so seamless, that all the little people making the starship work might as well be invisible.
On TOS this one episode, Chekov pushed the torpedo button, and then the camera rolled down to the torpedo bay, and there's a big flashing red light down there, and the guy in charge says, "load up another one and fire it off". So Checkov's button didn't actually make the torpedoes fire, it just made a light bulb in the torpedo bay "blink" which got the attention of the people who actually work for a living.
You're also talking about resource management which would fall under the XO's perview.