The bird will only be out when Nyx isn't in the room. The other point of research is getting a cage that a cat can't open, including access to food or water dishes. Nyx does sometimes watch my tarantulas but hasn't tried breaking into their cages.
Let me tell you a tale that hopefully will change your mind on letting a cat be in the same room as caged birds.
So, when I was younger I used to have budgies. I also have two cats, one who loves to hunt every animal, and one who doesn't seem to mind other animals as long as they leave her alone. Well, since I was young and ignorant to the still present danger of letting my chill cat in the bird room, I left her alone with them (still in the cage) unsupervised while I was at school. When I came back home that evening I found the cage to be completely toppled over, budgies flying all over the room, and that very same "chill" cat running all over the room. But even if there is a cat-proof cage out there, they can definitely still reach their paws in there and scratch the bird(s). Which I'm sure in this case is what caused the cage to topple over in the first place. That old cage of mine just so happened to have guillotine doors so they escaped immediately.
If my cat was better at hunting, those birds would've probably died that day. It is for any bird's best interest to be kept away from cats (and any other predator animals) 100% of the time. You can have cats and birds in the same household, I still do, but please make sure they are never in the same room. Disaster could strike at any moment.
I hope none of this came off as rude, I have a tendency to give off the wrong tone over text, I just want the best for you and your future bird(s)!
