I see a nice jade...with some help, it will be really nice :) Trunks are quite thick (I think diameter is approx. 3-3.1"; calculated from approx. 25cm circumference)

Pruning is best done in spring - early summer, while plant is in active growth. It would also give you chance to prune off any new (if) etiolated growth.

Can you tell if it is a few separate trunks, or just one that branched? It would be easiest to divide if separate plants, while repotting. It could be cut apart if one plant, hopefully each part with some roots. I would do it in few stages: divide and repot, let to 'recuperate', grow roots, and then prune. Or other way around, but 1st suggestion may be better. Pruning first to get rid of any spindly growth, and then prune to get a shape you want - if you want to change the overall look of it. JMO.

It needs good light to grow compact. Do you have that? - maybe with help of some supplemental lighting?