I'm not sure a list of supported resolutions is relevant since full screen just scales up the game to cover the entire screen. Aka it doesn't change the actual display resolution, at least I don't think it does.
Here's the api provided by nwjs which you probably can access from the browser object.
I didn't notice anything to get a list of resolutions there.
If you really want a list of supported resolutions you could make a nwjs addon that calls winapi functions to get that info. I think there was a construct classic example that used some Python to do that, although the actual c code to do it should be pretty easy to find online.