If these are state roads, I don’t see what the Feds have to do with it.
But you are probably right, the Feds probably are paying for the camera equipment, which makes it a federal issue.
Crossing from one state to another involves interstate commerce, the regulation of which falls under Federal jurisdiction under the Constitution. If the state of New York wanted to impose a congestion fee on the bridges and tunnels connecting the NYC boroughs, that would not fall under Federal jurisdiction.