I'll add a few comments on my experience last year and earlier this year. I had no problems between Newark and Kearny/Harrison, but didn't find a good route from Jersey City to Kearny.
Between Newark and Kearny/Harrison, there are 3 bridges on local roads. I recall they do have metal grating, but have multiple lanes and traffic goes at reasonable speeds (30mph). I didn't have any problems with traffic in Kearny or nearby parts of Newark.
I rode from Kearny to Jersey City twice (Sunday afternoon, Sunday morning in summer) on Route 7. It was rideable in light traffic on a Sunday. Most of the way has multiple lanes and often a shoulder, but motorists drive 60 regardless of the 30-35 mph speed limits. I would not want to do this in rush hour.
The first time I folllowed the Google route back over Rt 1 & 9; it didn't occur to me that I was supposed to lift my bike over guard rails or that NJ tried to put bicyclists on sidewalks. (The sidewalks on the bridges in Harrison & Kearny have utility shed creating narrow bottlenecks.) I obviously survived, but it was not a ride I wanted to repeat even on a Sunday night. Other times I went, I was also returning in darkness so I took the PATH train.
Is the bike "path" from Jersey City to Kearny/Newark a ride you would do after dark?