How does erg mode apply resistance during the pedal cycle

I think your thought process is right, but the unanswered questions are:

  1. How frequently does the trainer measure flywheel speed and what is its sensitivity to react to changes in speed?
  2. over what time interval will the trainer adjust flywheel resistance over?

While it would depend a bit on the exact gear ratio you are in, a single full pedal cycle is going to lead to multiple flywheel rotations on all the trainers I’ve had.

During this one pedal cycle, there would be a small increase in flywheel speed at the ends of the “peanut” and a small decrease in flywheel speed at the indent of the peanut on the force vs angle curve.

If this small change in flywheel speed both lasts long enough within a given pedal cycle to be detected by the trainer, and is large enough to be detected by the trainer, then the trainer could still increase/decrease flywheel resistance within a pedal cycle, making the graph into a circle from a peanut.

Actually I think some power pedals can display force versus rotational angle data. Someone could figure this out for sure by going into erg mode and then graphing applied force as a function of pedal angle at both a very high cadence and a very low cadence. The two cadences would serve to make sure there isn’t a threshold speed whereby due to the sensitivity/frequency of measurement of flywheel movement, the behaviour of the trainer changes.