Sounds like a bearing inside the tranny, possibly the input shaft one.
Think of it this way, in neutral, clutch pedal out, it makes noise, the input shaft still spins in neutral. Clutch pushed in, the input shaft no longer spins, and no more noise.
A worn pilot bushing can make for choppy clutch engagement as the input shaft deflects a little bit. A worn throw out bearing makes noise when the clutch pedal is pushed as that is the only time it is spinning (when it contacts the PP).