Don't know how many times I have to say it: brake booster [ BB]. Based on the symptoms described in post #1.
Booster operation is quite complicated. Modern boosters are vacuum suspended, ie at rest both sides of the diaphragm inside are balanced by engine vacuum. When the pedal is moved, atmospheric pressure [ AP ] is admitted to the rear portion of the BB, & this force pushes on the diaphragm & BB pushrod, into the m/cl. The amount of BB assist is governed by valving inside the BB that regulates the amount of air entering the rear chamber. It should be obvious that if this regulating/reaction mechanism fails or becomes faulty.......you get the exact symptoms the OP is getting.