The traditional monologue, as used in TOS, TAS, TNG, Strange New Worlds, as well as the endings of Enterprise and several movies, can be taken as a sort of overall mission statement for the Enterprise, possibly even one that takes place in-universe.

If the other series-- Deep Space Nine, Voyager, Discovery, Picard, Lower Decks, and Prodigy-- had similar mission statements, how might you phrase them?