The apparent quantity of rebar is likely a trick of the angle of the shot. At that angle, you're seeing much of the 130ft span compressed down to a space that looks more like 5 or 6 feet.
Everything about this makes perfect sense:
1) Existing, historic railroad bridge is in disrepair and needs to be replaced. It was originally comprised of three individual spans with interior supports; the center being the longest and the tallest. Instead of supporting trains, though, now it just needs to support pedestrians (and maybe an ambulance - I've only had to consider that for pedestrian bridges when there isn't a reasonable alternative for emergency crews to reach pedestrians in distress).
2) The held a design charette to get input from stakeholders (note that non of the documents anyone has linked to are in any way 'final' or 'for construction' - they are all preliminary concepts meant to a)provide a sort of proof of concept that it could work and b)provide the bare minimum visualization necessary). I'm not a bridge guy, but historic building structures are my thing, so I'm accustomed to working with architectural review boards and departments of historic resources and the like. This is how they think: keep the old stuff if at all possible; if not possible, then the new must evoke the old to the greatest extent possible. Since keeping the old one was not at all practical, they went with a new version that looked similar. Nobody forgot to install supports. They weren't installing the girders wrong. The goal was not an efficient structure but a structure that reminds people of the old one. When doing these types of projects, it requires us to ignore some parts of logic lest we go insane railing against it.
3) Skinny webs really aren't a problem. They're used all the time to improve material efficiency. That's what those stiffeners are for. It doesn't take much to handle the shear in a steel girder like that. The problem is the detailing at the transition. A thicker web might have saved them, sure, but a more efficient method would have been to detail the stiffeners at that transition better. I daresay that's why the opening line of the thread from bridgebuster was "I think they forgot some stiffeners." An oversight in consideration of web buckling at that transition by the design engineer is the most likely culprit.