That is defintiely unusual.
I agree with you that the bunny is not newly-born (too much fur) but is too young to be out & about on its own (eyes closed, not enough coordination to reasonably go anywhere.
I don't think mother rabbits carry their babies around. So it may have crawled from some nest nearby, although I still find that puzzling.
Or maybe it was carried by some other animal, although I cannot think of why any animal would carry a young rabbit and put it in a chicken nestbox. I would expect a wild animal to eat it, and I would expect a pet to either eat it or play with it rather than putting it down and leaving it there.
For what to do, I don't know what to suggest, because I see problems with anything I can think of. Returning it to the mother is impossible unless you find the nest, bottle-feeding would be a lot of work with a fairly high chance of failure, and humanely dispatching it is sad.