Could someone clarify what the time scaler does?
For example, let's take a circle, insert it into a block, blur it, enable simulation for frame feedback, and hit play. The circle blurs and expands with each frame. I change the time scaler from 0.000001 to 100000 – no difference. The number of iterations obviously affects the speed, but changing the time scaler has no effect. I expected the time scaler to act as a multiplier for the effect strength or the number of iterations, but apparently that's not the case. So what does the time scaler do then? What does it scale?

it does scale the timestep, some nodes do have Scale By Timestep checkbox

so on your Blur COP check Scale By Timestep (note that even on Timescale 1 this changes the blur strength as default timestep is 1/fps, so adjust accordingly)
then if you play with Timescale you should see the difference