> But, if my memory is good, when Apple was fined in France, it was shown that the throttling was performed without consideration for the battery state. So was done even with a new battery (or the power cord plugged)

I don't think you're correct here. The way this behaviour was initially discovered was that a reddit user ran a benchmarking app before and after a battery replacement, showing a substantial increase to performance afterwards.

It would not surprise me if this only applied to first party batteries, though I have no information one way or the other.