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?
I don’t think that Deep Space 9 would really have one, since it’s technically only managed by Starfleet, but is otherwise an alien station. Starfleet assigning it a mission of their own accord seems like it would be overstepping boundaries.
Picard might similarly not have one, since it’s not really following the adventures of a starship, or even Starfleet personnel, for the most part. It’s focused around Picard himself, and him having a monologue/mission statement about himself would just be a bit silly.
Discovery’s mission seems to be something along the lines of “These are the records of the Starship Discovery, to push boundaries, and go where none have gone before.”