I have gotten enough stars during this tour that I've unlocked all the gifts available. I still have some stars from races that I've not fully completed yet - is there any reason for me to work to get all the stars in all the tracks, if I don't have any gifts left to unlock? Do I get anything for them, or are they useful later at all?
No. It appears that stars are only used for accessing new cups and tour gifts. At the end of the previous tour, the star count reset and stars obtained during the New York tour didn't count toward anything anymore.
I kept racing, and eventually if you get another star after you have all the gifts, a message comes up telling you you can't get any more stars past the limit (I'm guessing the limit is getting all the tour gifts), and you get 100 coins instead.