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: Ray Charles is the singer who performs this version of "Somewhere over the Rainbow" - this is not on the original movie soundtrack, but you may be able to find a Ray Charles album where this song is included.
I found an album by Ray Charles "Genius Loves Company By Ray Charles, Ray Charles And the Count Basie Orchestra" where "Over the Rainbow" is one of the songs, but it's not the same rendition as in the movie "Sleepless in Seattle." I can't fine the movie version anywhere.
Try the Ray Charles album "Genius Loves Company." It's a collections of duets and he sings "Over the Rainbow" with Johnny Mathis. It was supposedly recorded sometime between 2003 and 2004, but his lines sounds like what's in the film. So I don't know if it's just him reprising an older version he did that was used in the film, or if it's the older version with Mathis' lines mixed in. I couldn't find anything earlier.
Bishop73