High priestess of Yonada was informed that the ship was firing missiles at a potential enemy? No? I wonder why?
The Romulans (or rather, the Vulcans) were inventing indoor plumbing when the Dyson Sphere was ANCIENT. Wanna bet to the inhabitants the door was already an ancient artifact by then?
Anyway, I think that they tried to make it clear in the episode that the sun was in the process of having a major fit.
Which is a silly reason to abandon an artificial structure with the surface area equivalent to several thousand planets. A civilization that has the technology to build a structure has the technology to mitigate that problem. If that technology--or the knowledge to use it--has been lost, so too has their capacity to abandon the sphere or, for that matter, detect the problem in the first place.
I suppose it's possible some of the die-hard sphere-people were sitting in underground hybernation capsules on the off chance the sun didn't go nova, stubbon super-advanced aliens that they may be.
Or maybe the Enterprise' sensors just aren't up to the task of scanning the equivalent of every planet in the explored galaxy for life signs, in an environment they weren't designed for, in thirty minutes or less.
Look, ancient, it's a matter of scale. We're not talking about some "really big space station" type scenario. This aint the promelian battlecruiser, it's not the nuclear-powered garbage scow, it's not even the freaking planet killer. We're talking about an object whose surface area is the equivalent of the entire Federation, an object whose inhabitants have not been heard from in the whole of recorded history, from which no vessel has entered or left in a geologic age, of which there are no rumors or legends or even indications of existence. Your thinking doesn't even hold water for an artificial planet ("Paradise Syndrome" and "For the World Is Hollow") let alone something that could swallow every Federation world and still have room to spare.