As you can see from the video the bike sounds horrible imo. It only does that when the clutch is engaged and it sort of fades away as the bike warms up but the sound is still there. Bike has 39k km.
The bike was in neutral when you let the clutch out I assume? What happens when you let the clutch out and the bike is in gear, and on the centerstand? Personally I think I'd be looking at the clutch basket assembly. But absolutely don't ride it till you pinpoint the problem.
I agree that you need to open up the right hand side of the engine to have a look at the clutch basket assembly. That video sounds as if there's something wrong with the Primary Drive Gear. It sounds as if there's no damping springs inside the Primary Drive Gear are not doing their job. The VFR800 engine cylinder firing order is "lumpy" and results in one particularly big hit of power once every 720 degrees of engine rotation (this is when cylinder number 4 fires and then cylinder number 1 fires just 90 degrees later). If the damping springs in the Primary Drive Gear aren't working properly the engine will "jangle" the clutch basket exactly as shown in your video. And when you pull in the clutch lever it unloads the substantially, thus the quieter operation.