Hello My name isXXXXX will be glad to assist you today in answering your questions.
Did you here any power steering noise?
Did any lights come on the dash ?
Is the power steering belt still on the car seen where the belt gets stretched pops off usually no noise but, you loose power steering?
Normally on the 3 liter engine the suction hose small hose on the back of the power steering pump, gets small cracks in it and the pump starts sucking air in and over time you will get a power steering wine when turning the wheel all the way to the lock position. Now in your case if the fluid was a touch low from this issue and the wheel was turned all the way to the lock its possible the pump was damaged.
Now its never a good idea to turn the wheels all the way to the lock position and leave it.
Biggest issue now is if the pump is bad did the low fluid damage the steering rack (or gear) when it went bad. When pumps go bad they start to come apart internally putting small amounts of metal into the power steering fluid. This small metal flakes under pressure can damage seals and destroy a power steering rack.
As for the timing its possible, but unlikely, the power steering pump on that vehicle is not known for its reliability I have replaced more on that engine than on any other Audi. I would say its a bit small for the vehicle.
Now if the shop did damage the pump they are never going to admit it. That's the bad part.
If you have any more questions please let me know.
I would bet money they will tell you it was bad luck, but something does not make sense here
Power steering pumps don't just stop pumping, without showing some sign or making a lot of noise.
If they do decide to replace the pump ask them to make sure they replace it with a ZF pump that is the brand Audi uses you can buy it from many parts stores, but the aftermarkets don't last but a few years.