You are right, it is not a single plant, but a handful of branches stuck in some soil and allowed to root. You can do whatever you please. Break them up into the individual plants, repot the whole clump, or just do nothing at all: Jades are very accommodating. It sounds like you want to keep it together, so just pull it out of the plastic pot and inspect the root ball. If the whole thing is a twisted mass of roots, slightly loosen them, pruning any obviously dead ones, and pot up into something larger. If it is mostly soil with only a few roots, pot it into something the same size as the current plastic one only adding a minimum of soil.

Whatever you decide to do, provide this plant with as much sun as you possibly can. If you keep it inside, it will *never* get as much sun as it really needs. Direct sun outdoors is the only wat to provide Jades with a truly adequate amount of light. Just be sure to slowly acclimate the plant to brighter light over the course of a few days so as not to sunburn it.