Dino oil or synthetic oil, as you found out, has no effect on the issue, and it would never cause a noise like you describe. Also, if the Kawwy manual says to use 80W90 final drive oil, use that. Do not use much heavier 75W140, as it may be too thick when hot to adequately flow into gear teeth clearances when under load. Kawwy suggest IF, when changing the oil, if you noticed a furry metal mess on the drain plug or in the oil drained out, then it would indicate an internal issue in the rear drive hub. When you say "driveshaft oil" you really mean rear drive hub oil. the driveshaft on the VN1500/VN1600 runs dry in the swingarm.
The sound may be driveshaft noise, though driveshafts on the VN1500/VN1600 are not known to have issues unless the bike has real high miles on it, which your bike only has average miles on it for the model year. That's not to say that for the miles it could not be the front driveshaft u-joint. On the link below is a section for servicing the u-joint. The front driveshaft bevel gear is another known noise source, when the bearing is nearing its service life. Since you say the noise occurs mostly when you actuate the clutch lever, I'd also suspect the bevel gear bearing, and next the clutch itself, which could be the throwout bearing in the clutch.
When you pull in the clutch the throwout bearing is loaded by the action of pressing in the throwout rod. If the throwout bearing is worn or has play it can emit noise. When the clutch lever is out, clutch engaged, the throwout bearing has little load against it if any at all. So I suspect the bevel gear bearing and/or the clutch throwout bearing.
You can find out a lot here:
https://gadgetsfixitpage.com/
There is a section on driveshaft repair, and about accessing the front of the driveshaft to lube the u-joint. That also clues you how to access the u-joint area to check for abnormalities.