Warptorio then uses LuaSurface.clone_entities from the current_planet.surface to the new_planet.surface
Each new entity created this way has defines.events.on_entity_cloned raised for it.
In this event you need to simply update your internal caching and duplicate everything to the new entity so the 2 are identical, but on a different surface.
Cloning does not typically happen in normal play, but to test it without mods, you can use the Clone feature in /editor.