States are bound by the US and State Constitutions.
The NY Constitution includes First Amendment protections regardless.
https://dos.ny.gov/system/files/documents/2022/01/Constitution-January-1-2022.pdf
Chick-Fil-A has publically stated, as has Hobby Lobby, that they are closed on Sundays for religious reasons. So it most definitely makes it a First Amendment issue. NY would have no power to force them to open on Sundays normally. But in this specific case the businesses in those particular locations are contracted to the turnpike authorities and if they want to stipulate hours in the contract they are welcome to do so. Chick-Fil-A then needs to decide if they wish to participate under those requirements.