Name this engine noise, can't be good!

That last video may at the flexplate or the TC bolts. But it sounds even more like an exhaust leak. Quite a different sound that the 1st video. With that hole in the inspectoin plate it ought to be easy to rotate the crank a bit at at time and check the TC bolts and the flex plate. Loose flexplate to crank bolts requires separating the trans and engine.

Any chance this has a exhaust heat riser flap still in it that has come partway loose? If the thremo spring is still there, and it turns the flap when it heats up... that might be it.

This 'hot noise' ought to be better traceable; better doing that and pulling the pan to chase this hot noise does not make sense 'til you do more to localize it. If 'twer me, I'd get a wooden dowel to place against various spots and against my ear to try to localize this.

I hope you have some jackstands under there too, and not just the jack.