The brief
The A3 had developed unusual noises from the aircon, a rattle and a high-pitched squeal that came in when the AC engaged, and the airflow at the vents had dropped, leaving the cabin warmer than it should be. He brought it in. Those noises plus weak cooling point at the AC compressor. The compressor is the pump that drives the refrigerant round the system, and it runs off the engine belt with a clutch that engages when the AC is on. When its internal bearings and parts wear, it gets noisy and can't pump properly, so the cooling falls off, and a compressor that's breaking up can send debris through the rest of the system if it's left. A compressor making that sort of noise has had its run.
The diagnosis
A check confirmed it: the compressor was noisy and not building proper pressure, with the clutch and the internal parts worn. The rest of the system, the condenser, the lines, the evaporator, checked out, but with a failing compressor the system gets flushed anyway to clear any debris before the new one goes on. That's a compressor replacement, with a receiver-drier and a flush, not something you nurse along.
The work
The remaining refrigerant was recovered, the drive belt released, and the failed compressor unbolted and removed. The system was flushed to clear any debris, a new genuine Audi-spec compressor fitted along with a fresh receiver-drier and new O-rings, the belt set back up, the system pulled down to a long, deep vacuum, and recharged with the correct weight of refrigerant and the right oil charge. A check at the vents confirmed cold air at idle and no noise from the compressor.
The outcome
Cold air at the vents at idle, strong airflow, no rattle or squeal from the AC, and the charge holding. The A3 went home with the aircon working the way it should. A failing compressor only gets noisier and can take the rest of the system down with it, so changing it, flushing the system and recharging properly fixed the cooling and protected the rest of the AC.