Weird noise. Kinda sounds like a timing chain but I don't recall those having many issues on these engines. Anyway you can tell if it's louder near the bell housing, like maybe a clutch or torque converter noise?
My first thought was idler or tensioner pulley but without the belt ? Have you checked the dust covers on the back side I’ve seen them get bent and rub on converters or clutches. Could be a loose or stretched timing chain I’m assuming 3.8 probably has quite a few miles .
