"Eventually, this rail service could also take advantage of Staten Island's restored freight rail network and reach out to the Northeast Corridor line as well, strengthening Staten Island's connection to the regional rail network."
Unfortunately, that is unlikely to happen, since subway or light rail type rolling stock is not allowed to share tracks with freight trains, unless the passenger cars meet ridiculously high collision standards (basically, the train has to be strong enough to stand a 10 car train on end without the bottom car bending). And I think this whole "light rail" business is a bad idea, since Staten Island already has a perfectly good heavy rail line, and indeed much of the heavy rail infrastructure is still there along the North Shore Line, notably the viaduct through Port Richmond. On the other hand, they could extend the HBLR over the Bayonne Bridge, and provide a transfer with the North Shore Line. It's unfortunate that thanks to Bob Moses it is impossible to run a subway line over the Verrazano Bridge, but it might be possible in the far future to build a tunnel from St. George to Bay Ridge.
Another option, somewhat from the realm of fantasy, is to replace the Staten Island express buses with light rail, with street trackage feeding into a line in the middle of the expressway, and then going over the bridge, down the Gowanus Expressway in Brooklyn, and then through one of the Brooklyn Battery Tunnel tubes into a street line up, say, a Broadway that has been dedicated to pedestrians and light rail.
I think the bus route, if successful, would be an easy gateway to eventually extending the HBLR over the Bayonne Bridge (which was actually built to hold rail). And then eventually linking that bus/light rail to the existing Staten Island Rapid Transit and/or the North Shore extension (light or heavy).

You are right about light rail sharing with freight. I was more thinking that they could build new light rail lines along the same ROW. It would either need to use new tracks or be heavy rail. Frankly you are right that considering how much heavy rail exists, it might actually be a better fit. I'm not sure if the politicos have picked up on that nuance or if they just assume light rail is easier in principle.

If Staten Island we a part of New Jersey instead of New York, I'm sure NJ transit would already have several rail links to their regional rail hubs in Newark, Secaucus, Jersey City, etc.

Re: Verrazanno - The Tunnel would be cool! Until then a dedicated bus lane can do a lot of good work during rush hour.