Revealing mistake: In the final scene when Annie and Sam are exiting the observation deck coming towards the elevators, the New York skyline backdrop which should be visible behind them is missing, and the entire sound stage wall can be seen beyond the observation deck safety railings instead. 'Although the exterior and lobby of the Empire State Building, 350 Fifth Avenue at 34th Street, are the real thing, a slightly larger replica of the Observation Deck was built in a hangar at Sand Point Naval Base on Puget Sound just northeast of - where else? - Seattle.' https://www.movie-locations.com/movies/s/Sleepless-In-Seattle.php. (01:39:35)
Answer: It's called Empire State Montage by Hugo W. Friedhofer.