I tried attaching a camera to a path, using the circle spline and it works, except around frame 135 their is a weird wobble where the camera jumps.

I can't seem to figure out why it is doing this. Guessing maybe something in the circle properties, but not sure.

Attached is the file

Yep, I see it. Not sure why?

What I did was to zero out the Translate and Rotate on the camera object then I picked the platonic as the Look At for the camera. The gives a nice smooth turntable style animation with no jump.

I did what you suggested and it seemed to work. Have no clue either because nothing was keyframed. But works great now