I don’t have any direct experience, but I would say you need to make sure the generator is properly ventilated to the outside world.
Although it was different circumstances a couple of guys in a nearby town died from carbon monoxide poisoning because they were using a generator to pump out a flooded basement.
Have you thought about solar power at all?
You’d need to work out how much electric power you’ll need in the observatory, and then match to batteries and solar panels that would be sufficient to fully charge in a day or so.
Will be interested to hear how you get on, and what you decide to do in the end.