I’ve driven on the Thruway before. As I recall, their rest stops also have convenience stores.
My impression from various sources is that a convenience store and multiple food outlets will be at the locations.
It doesn’t appear to be a matter of driving up to a simple rest stop and the lonely Chick-fil-A being closed on a Sunday.
I was on the NYS Thruway before and after Christmas this week. Along with the Thruway rest stops, there’s exits for towns and cities. No one is going to starve to death if Chick Fil A is closed on Sundays.
In fact, take an exit and hit up one of the mom and pop restaurants in town. You’ll probably eat better, help support a family, and get to know more of NY other than I-90.