I recently came across a cone-style LSD for 091 gearbox and couldn't find any information online, so I thought I could be useful to share some pictures.
From outside


here you can see the springs to preload the cone style clutch

springs actually push against the sidegears

and here is the cone. When torque is applied to the diff, the cones below the side gears are pushed harder against the carrier, acting as a clutch to lock the sidegear to the carrier. There are oil galeries to keep them lubricated.

Everything disassembled

Sidegears next to the cones

Another view of the clutch

Output flanges are difficult to rotate separately because of the spring preload on the cones. Holding the diff by hand, I can't move them. The diff gives a good impression, I wonder how it behaves on the street

This diff came with a bunch of other VW LSD from a workshop which used to repair military vehicles.
Hope that it can help someone.