in 1899, probably the only place you could see a passenger pigeon would have been the Cincinnati Zoo.

They were extinct in the wild by 1895.

https://en.wikipedia.org/wiki/Passenger_pigeon

I believe the entirety of the game is set in a fictional equivalent of east of the Rockies, so I doubt it.

There's really not much equivalence to anywhere, other than the different biomes resemble ones you'd see in the US (outside of a side mission to Guarma, a fictional island near Cuba). There's a swamp area similar to Louisiana with a delta city called Saint Denis (pronounced San Da Knee). To the West (yes, West) of that is the 'southern' town of Rhodes with plantations and antebellum houses. Nearby is a former Civil War battlefield. Further west is the typical wild west frontier, with the nothern areas being colder and mountainous down to the more southern areas being grass and desert plains.

In game there is talk about real places (like New York, Cuba, Tahiti) but there is little context to where those are in respect to where the player is.