There may be issues at those places in NYC, but I don’t know that they are related to traffic from NJ. Friends that ride the rails in from here describe lower ridership than 10 years ago.
NY didn’t want to share revenue for a second bridge (as they do with the GWB), so they built the Tappan Zee Bridge at a point where both sides are in NY - and the river is VERY wide (which brings a whole slew of problems with it). Now they want help repairing/replacing it...
Actually the Tappan Zee was built where it was because engineering-wise, it was an ideal spot. Though the Hudson is about its widest point in that area, the waters are comparatively shallower making the bridge easier to build. The new Tappan Zee is already well under construction and the progress being made is incredible. I’m thinking they are afraid the old one might fail at any minute.