Before you worry anymore about how ruined the car is, I'd take it to a reputable independent and get a verdict from them. It's entirely possible that the damage is very superficial, and apart from a new diff coupling, (and uprated bolts), you may just be looking at a bit of cosmetic damage that isn't actually that serious.
Remember that Audi employs "technicians", (mechanics), in its dealerships, not engineers. They're not interested in fixing any damage, they'll just replace any parts that are at all compromised with new to avoid any future issues, (and associated labour costs). It's easy to see how the warranty claim can run into thousands when you're just swapping parts out for new. Personally, I wouldn't place too much value in their judgement.
This is where an independent shines. They're not using a predetermined approach from Audi procedure manual that removes decision making from the hands of the mechanic. They're using experience and skill to decide the best way to fix the problem. I wouldn't be surprised if the whole debacle ends up costing just hundreds, (rather than thousands), and you end up with a car that won't suffer the same problem again.
This my friend is quite possibly the soundest bit of advice I've read on a forum in a long long time. Top drawer.