The brief
The A7's aircon was blowing hot air, and the cause of that can be a few things, a leak, a sensor, the compressor, so a proper diagnosis comes first rather than just topping it up and hoping. He brought it in. The diagnosis here pointed at the compressor. The compressor is the pump that compresses the refrigerant so the aircon can carry the heat out of the cabin, run off the engine belt through a clutch. When it fails, internally worn or the clutch packed up, the cooling drops off, and a broken-up compressor can leak debris through the rest of the system. A failed compressor doesn't recover, so it needs replacing, and properly: the system flushed, the receiver-drier renewed, and the whole thing recharged.
The diagnosis
A check confirmed it, the compressor wasn't building proper pressure, its internals worn, and it had let a little debris into the lines. The condenser, the lines and the evaporator checked out, but with a failed compressor the system gets flushed regardless before the new one goes on. That's a compressor replacement, with a fresh receiver-drier and a flush, not something a recharge alone touches.
The work
The 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 cooling, no noise from the aircon, and the charge holding. The A7 went home with the aircon working the way it should. A failed compressor only gets worse 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 aircon.