This is a regular issue and source of much confusion, and the discrepancy comes from iNaturalist using Google Maps for search on the main location search bar versus the locations that they have in their database. (https://forum.inaturalist.org/t/place-new-york-city-doesnt-work/26533) It’s mentioned in that thread that iNaturalist has plans to address this in a future update to the Explore page.
If you open the Filters then More Filters > Place and enter New York City, NY, US into the Location it will give you what you want.
https://www.inaturalist.org/observations?place_id=674&subview=map