By the looks of rotted trunks/stems, I would suspect also rotting, mushy roots. Therefore, it would be time for a complete dismantling if it were mine. Remove it from the soil, gently work the soil away from the roots, remove all dead root and branch, then re-evaluate for the repotting.

If it comes apart into several plants that were potted together, you could redo pot everything up together, or you could start several new in separate pots. If the mass of it is all basically one now, then keep it together and get rid of as much of the old soil as possible without significant root damage, and repot the mass of it.

What kind of soil are you planning to use if you repot it?

I'm planning to use whatever is best... I can shop if needed. The only thing I have on hand is a mixture of one part peat moss, one part vermiculite, and one part compost.

Also, vermiculite collapses relatively quickly leading to loss of air pockets, so for a jade which can spend many years in one pot, it's not the best substrate to include.

For potted succulents, it is better to have mix of more inorganic ingredients - gravel, turface, perlite, scoria, pumice...

I'll start looking for ingredients for Al's Gritty Mix. I also want a different pot. I don't mind this one, but it doesn't have a tray underneath, and I'm not sure how that will work with watering.

Maybe as wide, but shallower.