I can see why you're at a loss!
It sounds like the starter is engaging, and the rising/falling gear whine suggests that it's doing work. But if the starter's not spinning the crank pulley (I can't see in the video but I assume this is the case, given what you've tried so far), either the crank's not moving or crank snout picked a very odd time to shear off, and if you turned it over by hand and the crank pulley didn't wobble around like it wasn't connected to anything, the crankshaft's not the problem. That leaves the starter and the flexplate.
If it's the starter, my guess would be the sprag (one-way) clutch in the pinion. If the shop that tested your old one just did an electrical test, they could've missed this. I'd expect your replacement to have sorted this out, but if it's reman, maybe they didn't test the clutch in that one, either. That said, when the sprag went on my '95, it made a godawful metal-on-metal shrieking noise entirely unlike your noise. So the other option is that the ring gear has separated from the flex plate. That would require eight (I think) separate welds failing. I haven't heard of a Pathfinder having flexplate issues, though I have heard of other vehicles' ring gears breaking up or even falling off when a built-up engine backfires while starting or if there's something horribly wrong with the flexplate. Maybe if your trans went with a bang rather than a whimper it could've warped the flexplate enough to crack the welds, but I'd be surprised.
What I'd do is drop the starter again and put a paint pen mark on both the ring gear and the inner part of the flexplate, and then see if you can shift the ring gear on its own with a screwdriver. If that checks out, put the starter back on and try to crank it again, then pull the starter again and inspect. If the paint marks separated, the flexplate's hooped. If the marks didn't separate, but stayed where you put them (suggesting the flexplate as a whole didn't turn), that suggests you got a bad starter.