I like it a lot - like RL said, the dialogue sounds natural; and I enjoy the subtle reference to the Falcon from the stormtroopers - but (nitpicking) it feels a little awkward to base it all around the one hangar. “Sir, she’s 100% heading for this hangar, no doubt about it!” “Sir, she, uh…she wasn’t there. So most of us left.” “OH WAIT CRAP SHE’S THERE NOW MOVE MOVE MOVE!!!”
Maybe make it more vague - “Sir, the prison level is on lockdown. All troops are on alert; she won’t escape.” “Sir, Captain Phasma has ordered a full sweep of the base. She can’t hide forever.” “Sensors triggered in Hangar 718. We’re searching the area.”
The reason I removed the official line (the last suggestion) was because Rey had just escaped the cell and presumably wouldn’t have managed to get to the hangar at that point. I do think it’s important to reference a hangar since the Kylo update 2 implies prior discussion, the question is how best to do that.
“Sir, the only way out of the cell block is through hangar 718. We’re searching the area.”
“The longer it takes to find her, the more dangerous she becomes.”
I don’t think you need to reference a hangar beforehand - honestly, I think that makes things a bit more confusing. If she needs to go through Hangar 718 to escape, why are the First Order even bothering to search for her? Just set up there and cut her off. But then later, Kylo says to put “Every hangar on lockdown,” as if he doesn’t know that she has to go through this one specific hangar. And when “Sensors are triggered in Hangar 718,” it’s just treated as some routine disturbance that a couple of troopers investigate. All three interactions just sort of contradict each other.
Kylo bringing up the hangar in the second conversation just sounds like he’s saying, “Whelp, we didn’t find her yet. What’s her next move going to be? Oh yeah, steal a ship.”