What dramatic/theatrical genre would you categorize Plenty into?

I would suggest that Plenty is a tragedy. It is a tragedy both for postwar Britain, in which the play is set, and also a personal tragedy for the protagonist Susan Traherne. In fact, the two are inextricably linked. Susan's descent from boredom and moral apathy into outright madness can be seen as symbolic of the slow, steady decline of Britain as an international power, which reached its nadir in the Suez crisis of 1956, when the whole country suddenly realized that the heady days of empire were well and truly over.
The figure of Susan's husband, Raymond Brock, is also highly symbolic. Raymond, a weak, impotent man of only middling ability, can be seen to represent the British upper class and their failure to adapt to the harsh new realities of the postwar world. Faced by economic stagnation and a loss of international prestige, the British establishment simply muddles along as best it can, managing what seems to be a process of inevitable decline.
The greatest tragedy of all, perhaps, is Susan's chronic lack of fulfillment. It is from this fundamental deficit that all her problems ultimately arise. She craves not just excitement, she wants the overriding sense of purpose she enjoyed when she risked her life for the French resistance during the war. No amount of adulterous liaisons can ever begin to fill the gaping void in her soul, nor can she ever hope to fulfill her seemingly endless quest for plenty.
Susan, like her country, once had an important role to play. She knew where she stood in the world, and that gave her life a sense of purpose and meaning. Unfortunately, the empire is no more. Neither Britain nor Susan have been able to find new roles for themselves.