Save Our Ship v2 has been released: https://steamcommunity.com/sharedfiles/filedetails/?id=1909914131
With this mod, any ship you launch is saved to a file. You can then start a new game using this ship to continue your colonists' stories on another world! Research, player faction data, and pawn relationships are all carried over.
SOS also includes new ship parts which allow constructing a proper interior. Any building or item placed atop a hull tile is saved with the ship - letting the colonists bring their favorite art, their workshop, and all the supplies the next colony might need. Cryptosleep caskets can be built inside a fully sealed hull at reduced cost.
====Technical Details and Known Issues====
This mod requires HugsLib.
"Loose" pawns aboard a ship won't be saved with it (they'd die during the interstellar journey). Put your colonists/animals in cryptosleep caskets.
Hull tiles can only be placed in a room fully bordered by ship parts. Placing a wall, nutrient paste dispenser, or any other building which counts as a solid wall will prevent placement of hull tiles in that area. Hull tiles automatically create roofs for themselves, which may cause compatibility issues with roofing mods.
Starting a game with a landed ship prevents new pawns from being created at game start. Colonists can still join later, of course. Ship starts are also incompatible with "start with," "start with animal," and "start near" scenario components.
There are many ways in which a third-party mod could store world data. If it's not saved inside a vanilla data structure (specifically the pawns themselves, a building on the ship, a faction def, researchManager, taleManager, or playLog), it won't come with the ship, which could cause issues with those mods.
Many NPC pawns from the old world will be missing when the ship lands, which will produce warnings if developer mode is enabled. The game cleans these up automatically.