They live in space. It would have to be a rather antiseptic environment, generating minimal dirtiness to begin with. Scrubbers filtering the air of dust, particulates, pathogens, etc... Note the bridge plaque had no actual dust on it. It's a symbolic gesture. Molecular decompiling handles all waste removal. So the ship does manage the majority of environmental control itself, & litter is an unlikely issue, as the majority of inhabitants are crew, who are responsible for tidying up after themselves
We do see however, that the ship has maintenance crews, who are likely responsible for not only technical tasks & repairs with computers & engines & such, but also with the ship itself, as in carpets & floors that need treatment or replacement from wear & tracking in of exterior materials, & they likely have a great deal of tech which makes it more maintenance than housekeeping, perhaps even some robotics that sweep/polish/shampoo/vacuum etc...