The carbon comes from the fuel. Burning a ton of jet fuel will release the same amount of carbon regardless of the plane that burns it.
Taylor Swift's plane is a Dassault Falcon 7X. It weighs around 17 tons and seats 12 to 16 passengers.
Her plane burns 60% less fuel than a 737 MAX 8. However, her plane holds 9% of the passengers of the MAX 8, so its far less efficient per passenger than typical commercial aircraft.
Private planes are not a huge contributor to carbon emissions in comparison to others. They're bad, obviously. But there are far more commercial airplanes, and they fly much more frequently than private jets.
Private jets get people's attention. One person being directly responsible for that much carbon is notable is unconscionable. But it's the scale of transportation overall that is the issue.