Either way, TwinTurbo’s or Nevada’s ideas, needing a new booster wouldn’t be due to something the shop did incorrectly imo. Just a part that was near the end of its service life went bust as part of a normal brake job. I’ve had to replace/rebuild brake master cylinders as a result of the disturbance they take as part of a brake job. I’m currently fixing a problem with a household appliance that was a result of a disturbance to the appliance caused by my fixing another problem. All in a days pay. Quite common as mechanical stuff ages.
Yep I agree that problems may develop and you just have to expect you may need some more parts. One of my first brake jobs after my Morris, was on my 68 Dart. It was only four years old but several of the bleeder screws were frozen solid and twisted off. I had to put new cylinders in. Maybe it wouldn’t have happened to a pro but I would expect to have to pay extra for something like that.
Couple of problems with that based on what OP said. OP did not mention the pedal going to the floor but did mention that this happened the first time OP drove the car after the shop was done with it.
Assuming that’s accurate, what happened is that the mechanic pressed on the brake pedal before OP did, as he was driving it from the bay to the front. Setting aside the fact that the mechanic should have known better and not pressed the brake pedal to the floor, what this means is that if your theory is correct (and it very well may be) the booster diaphragm tore while the mechanic was driving it.
So why did the mechanic not recognize the symptoms of the torn booster and immediately tell the customer “This happened, it sometimes happens when you work on the brakes, and we’ve gotta fix it.”
Instead they turned the car over to the customer and stayed silent about it, which is dishonest move number 1.
Like I’ve said throughout the thread, it’s highly doubtful that the mechanic actually broke the part while replacing the pads. But that doesn’t mean the mechanic didn’t do something dumb, like your suggestion of slamming the pedal to the floor carelessly, to break it after the job.
That the dishonest in its dealings with OP suggests that either this happened, or that it’s at least reasonable to suspect that something shady happened because if you’ve done everything right, why do you need to lie (either directly or via a lie of omission) about what happened?
Noisy shop, maybe didn’t hear it.
He didn’t use the brakes to stop the car in the parking lot? 
I’m not even a mechanic but I can’t hear the wear indicators on brake pads. My wife has to tell me.