Few emotions nourishes the soul, as that of pride that comes with earned success.
Trying to make inanimate characters take on human personalities is a long-running theme of David's photography, and humour is his favourite emotion to stimulate in order to achieve that.
Here, Vader has a Stormtrooper to shield him from the rain and the trooper does his work but feels a little embarrassed by his circumstances.
Why would a dark lord of the Sith need an umbrella? Because he can.