I dont do NY, with how busy we are with covid demand its next years work already. That is a serious mess. You have a great case for legal recourse. They knew amd clearly hid the sinking corner. If it wasn't disclosed they are on the hook. I think NY law entitles you to attorney fees as well I'd bet a lawyer would take this on based on contingency of settlement payment.
For a steel wall pool it's a big repair honestly. That would take my crew anout 2 weeks. You have to remove all coping and pavers and lose the newer liner too. Dig behind the walls to get to the collar. Its obviously either missing of poorly done thin concrete that broke off and let that corner sink. The wall panels would be removed and floor cut back. New base and level then re attach wall panels, new concrete collar, patch floor. Backfill, compact, set coping and pavers then hang liner and fill. That is best case scenario hoping you dont hit plumbing or electrical doing the repair amd the coping/pavers are reusable otherwise a patch will be obvious. And that's counting on reusing the existing pool frame if it's not tweaked or rusted out.
All this is after fence removal and building a new engineered wall that is stamped off by a licensed PE. That's a job itself then reinstall fence. That's a huge repair overall 40k wouldn't cover it. More than half would just be the wall with the tight access. Go after the previous owners dont let them get away with it