With a bad master cylinder, pedal goes to the floor with the engine off and doesn't brake well
With a leaking master cylinder the pedal held down will not keep the truck stationary in gear
With a bad booster, the pedal is hard to push down with the engine on and doesn't brake well
With a leaking booster, the pedal get harder when held and hisses while the engine is running

That established...

My truck brakes just fine, the pedal is hard to push repeatedly after the engine off, doesn't sink, and holds vacuum for days... but pushes almost to the floor with a loud huff when the engine is on and has no hiss.

Where do I start trouble shooting?

96 3.0

 

Not sure on the other stuff

Brake pedal is connected directly to the master via the pushrod, engine on or off the pedal shouldn't go to the floor, if it does then there is a leak in a brake line, if no leak then Master is bad

So check master fluid level and all 4 wheels for a leak
Then look for leak between cab and drivers side rear wheel, rear brake line, it can rust out

Power assist is just that, it uses outside air pressure to assist driver pushing down on the pedal, it does that by sucking out air from one side of a diaphragm, engine vacuum, so when you press on the pedal air from the cab rushes in and "assists" you in pressing down on the pedal

If pedal goes to the floor, with assist, and doesn't pump up with repeated pedal pumps then Masters seal is most likely the problem, so piston seal is allowing piston to move thru the brake fluid, its not pushing fluid out to calipers/slaves so pedal goes to the floor

If it does Pump Up then could be a rear slave is stuck open, so you have long pedal travel to fill it up then once its full pedal feels high again