Seals fail now and then, it's not uncommon. To answer your question about warranty coverage, I would say not unless you have some sort of extended service plan or aftermarket warranty would it be covered. Factory warranty was only 3 years, 36k . You are well beyond both those parameters.
I think your estimate for just the seal is a little on the high side. You should not have to pay over 1.5 hours labor for that operation, the seal is typically $25-30 range. I would think more like $150 would be in order.
If you have rear axle damage, is the rear end making any noises, shuddering or binding? You would be looking at a larger bill. It would be safe to estimate roughly $1400 for a bearing only overhaul of the rear axle. I suspect you probably only have a leaking seal, or maybe a grooved yolk. Average labor on that job is around 7-8 hours, 300-400 for bearings, pieces ect. Gear lube is synthetic 75-140w and is spendy . It runs around $20 a qt. You would need 3-4.
Take it to someone reputable. Have them asses what is the cause of the leak, and overall condition of the rear axle, unless you are capable, then do it yourself.