This whole article is about private information. The flight data is, as enough people already told you, not private information. For good reason.

Not really. There is no guarantee that Elon is on the plane. He could loan it to a friend or one of his companies VPs. The plane could be at it's home airport, fly to another airport to pick Elon up, fly to a third airport to drop him off then return to the home airport. Elon would have been on only one of the three legs.

What's in the plane is private, where the plane is isn't.

Twitter (and Musk) has access to pinpoint each of their users with the same precision, I feel it's a poetic balance.

whose, the airplane's?

This is all public information already. There is no invasion of privacy.