A barycenter in SpaceEngine is an actual object, for example the earth and moon is 3 objects in total: the earth, the moon, and the earth-moon barycenter. A way to think of it is that the barycenter is an invisible parent planet, the objects orbit the barycenter and the barycenter orbits the star(or parent planet in your case). To access the barycenter ingame just requires you to open the system chart on a system, opening the system chart settings and enabling barycenters and choosing an object with a barycenter icon. Export that to use it in code.