Not the nominator for either of the Trek items listed here, but I can tell you there are no specific groups of Caitians in Prodigy. So, the nominator is likely just looking for original members of that species.

For the Enterprise, it is not a sentient character on the show, but it is not uncommon in this fandom to write any of the ships as sentient, and/or to write a fic where the ship is itself the focus or plays a large role in the life of a character.