Sukuna does die in the manga. The way it happens is quite dramatic and ties in with many other elements of the story, adding depth and tension to the overall narrative.
Barrett was defeated by Luffy in One Piece's movie, Operation Fever. In the movie, Barrett fought against Luffy and his other companions with his powerful strength and lonely faith, but he ultimately failed. Although Barrette was powerful, his failure was reasonable. He was too lonely, and the power of unity couldn't be defeated by loneliness. The reason why Luffy was able to defeat Barrette was not only because of his own strength, but also because of the help of his companions. The search results didn't provide any specific information about how Barrett was defeated.