Updated: Aug 24, 2019
There basically is no such thing as 'waste' in the Forever Fleet, with the vessels designed to retain and reuse everything.
Big holds will be used to gather and robotically sort waste, not only waste from use by Forever Fleet inhabitants, but thrash also scooped from the ocean and received from waste dumps around the globe for free in return for keeping much of the resources therein.
Not much sorting will be expected from inhabitants (it rarely works well anyway), since robots combined with plasma gasification can handle almost anything, even including dangerous chemical weapons, and turn it into raw materials without polluting.
When not helping with disasters, the surplus energy of Forever Fleet ships is mainly used to sort through this waste, extract useful materials, reform raw materials and feed necessary production, as well as eliminate the toxicity of any last remains for isolated storage on land where it can do no harm.