This is a horrible spot imo. I never fold turn here, that's just so gross it's another ace here sometimes I think. Although his line defo screams set so I can see why you folded river.

Given we're getting 3-1 on the river I'd just go ahead an pay this off, although it is really gross and I would expect to lose over half of the time at least. Not sure we can fold to the half pot shove though on the river without some sort of read that villain would never donkilly do this with AQ, AJ or air.