I think a key point here is that the camera is behind a window and not actually 'in' with the birds. This offers a high level of protection to the camera, which would need to be considered if it were actually inside of a cage. That said, a bullet isn't a bad idea since they can be relatively small, use integrated IR and have protection from the bullet casing.
Depending on how big the nest areas are, it may require a fairly wide angle of view to capture everything with a single camera (assuming that is the goal). I would assume little obstruction inside of a nesting area, but in a larger sized estuary where it is more of a 'natural habitat', I can see things like trees and bushes, etc. becoming obstructions to the camera FoV.