Is it a good idea to ground a heat sink?
If users can touch the heatsink, such as at the back of some linear power supplies, it should be grounded and electrically insulated from the semiconductors mounted to it.

A common way to do this is by using aluminum oxide plates, TO-220FP packages (plastic housing) or a sil-pad.
Or semiconductors, such as IGBT modules, that are mounted on a ceramic base.

The power supply you have shown is intended to be mounted inside an enclosure, where users cannot touch it.
Heatsinks inside power supplies are often not insulated, since it add costs and users are unable to touch it anyway.

So no, it would not be a good idea to ground this heatsink, as it will most likely cause a short circuit.