It is not illegal to track someone's flight; this is publically held information by the FAA. Private planes are part of a taxpayer funded network of airports, air traffic control, etc; all of which need to be able to talk to each other openly and track which planes are going where in order for that system to function properly.
Hiding this information is a public safety issue; if no one knows the plane is there, it creates problems for the safety of that plane and the safety of other pilots flying nearby. If no one knows the plane is in the air, then some hobbyist doctor in his small aircraft could ram right into it and boom, you've got a midair collision raining aircraft parts down on a small town in 'flyover country.'
Funnily enough, the flights are also tracked publically FOR THE SAFETY OF THE PEOPLE ON THE PLANE. If there is an issue with the aircraft, local emergency responses need to be able to identify where the plane went down as quickly as possible in an attempt to save lives. Otherwise, you could end up in a situation like the infamous Malaysia Airlines Flight 370. Elimnating public tracking of her aircraft would probably put Taylor in a lot more harm than broadcasting what airports she flew into/out of ever could. Again, public safety issue.
The FAA was hardline on this during the 2008 financial crisis when lots of major bank executives tried to divert public opinion by scrubbing their flight records (for some reason people were upset that the banks who'd just gotten a bunch of taxpayer bailout money were taking lots of private flights!)
A few years back when Elon Musk claimed this exact same Florida student was posting his 'assasination coordinates' and tried to get legal recourse against him, his legal team quickly found out he had no standing to sue. All Musk could do was ban this kid from twitter.
Again, this information is tracked for public safety. It is legal and important that this tracking information is available. This doesn't stop being true just because the rich person complaining is someone you personally like.
If Taylor Swift was really worried about her safety, then she would do what a lot of other rich people have done these past few years and charter her private flights. That way she's not the owner of the aircraft and, while the plane is still visible, it's unknown who's on it. The CEO of Apple pulls this move, no reason Taylor couldn't do the same.
But she's not doing that. Because this isn't about her safety. This is a petty move because she's upset the whole 'private plane impact on climate change' discourse dinged her reputation a few years back.
And rather than selling her plane or taking less private flights, she selfishly wants to keep one of her favorite toys.
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