Re: mantle of leadership/cloak of comfort/ robe of responsibility
A mantle is a type of clothing generally worn by bishops, nuns and monks in certain Christian churches. The phrase "passing the mantle" originated in the Old Testament of the Bible, and was symbolic for passing the authority. In its modern usage, it means much the same thing, but doesn't refer to a literal passing of a piece of clothing, but a metaphorical passing of responsibility.
So "the mantle of leadership" simple means "the responsibility of leadership." The rest of your sentence is merely carrying on the same metaphor, but using "cloak of comfort" and "robe of responsibility" for stylistic reasons. Mantle, cloak and robe all mean similar things, but are all being used metaphorically here.