Had – on one mountain bike – really problems with this issue as well.
Front brake was much worse than rear so.
Guess it’s also an resoance issue of disc, spokes, rim, fork, frame, tire.
In other words: every bike is different….
Easy to change: the brake disc
Solution I found:
cheapest Shimano disc and cheap organic pads.
The Shimano disc I use appear to be very stiff in rotational direction. Some others are very “soft”. Had problems with the soft discs (the ones where the manufacturers nearly cut all steel away).
Sintered pads, this bike: not possible to use them in wet conditions. Was a nightmare.
But that’s typical where “resonance” is a problem. Changes in the system will tune the resonance.
Sintered pads work on one bike – on the other you have to use organic ones. Third bike has no problems at all (like my cheapest bike).