So, here is my latest update.

The car was running very rough at idle and seems to be getting worse. When the car is in “drive” at idle, it started developing a loud “chirping” sound that gradually got louder.

I took it back to the shop that did the timing belt, water pump, and replaced 2 motor mounts.

Long story short: The new motor mount/strut on the passenger side of the motor was adjusted properly (front to back), but the adjustment (side to side) was a little close to the motor. It was just enough that the idle would cause it to make contact and really vibrate the car.

After a readjustment, it idles A LOT smoother. However, there still is a bit of a shake at idle, but nothing close to what it was. They claim that if I replaced all of the mounts, it would smooth out like a new neon.

Based on what I experienced just with just one properly adjusted mount/strut, I totally believe it.