(^ My 2004 Prius - since sold)
Friction braking issue: The amount of creaking is proportional to how hard I press the brake pedal.
I disassembled the brakes and found that there was a layer of corrosion on the anti-rattle / anti-squeal shims:
(For illustration only: I recall my 2004 had only 1 shim per pad, not 2 as shown.)
I used a grinder with a wire wheel to clean the shims to bare metal, greased both sides liberally and re-installed.
After reassembly, NO MORE CREAKING. My guess is the creaking noise was the sound of the corrosion compacting.