First off, great job saving it & being so patient!!! I would recommend posting a picture so we can have a better idea of what you are working with over there. Generally, the recommendation is to not repot until spring unless you think it will be detrimental to the plant to wait. Also, the general recommendation is to not prune and repot at the same time. BUT those are GENERAL. We can't give proper advise without pics. Or at least I don't think I can. :-)

I agree, you will get great advise on here, but, we really do need to see it, look forward to your pictures. From the sound of it you have done good so far :) so it may just need tweaking.

Gill UK

Oops, didn't even think about pics. So I just took a couple. This is the whole pot- You can see the new bits in the upper left corner of the pot, and tiny one in the bottom center, and one older leaf bit on the right- I could have sworn the older leaf bit also had new growth sprouting off of it, but maybe one of my cats got to it.

Closeup of the baby bit on the bottom. Sorry it's not a great pic, I haven't had coffee yet.

pic of the larger bit..

Great job saving this jade! They are such resilient plants and can bounce back from neglect better than any other I have seen!
Definitely needs to be transferred into a much smaller pot with a better draining soil. It is recommended to wait until Spring and I think it will survive until then. Does that pot have a drainage hole? Just make sure not to over water or you will be dealing with root rot as well. With that big of a pot and that medium it will take a long time for the soil to dry out between waterings. Keep it in the sunlight and make sure there is plenty of airflow. Also, try to keep as much of the dead material out of the pot, that could also rot and attract pests and fungus.

Yep, the pot does have a drainage hole, and it's sitting in a clear saucer, though you can't really tell that from the pics. I have no idea what the soil is that it's planted in right now- might be just regular potting mix. I think it might be the same soil it's been in for at least a few years from when my sister originally inherited the plant from a friend.
What soil mix am I looking for when I go to repot it? Cactus mix? Or can I mix sand into regular potting mix? Or what?

And it is in the sunniest location in the house, my south facing windows. You just can't really tell that either because the day is so overcast and it's snowing.

Be very careful watering it until spring. That soil looks very water retentive and can lead to rot. Make sure you're taking long breaks between wateringse

As far as the new soil to use. The Jade would most prefer Al's Gritty Mix. Search the forum on here and you'll find all the info you need. But it is a bit more expensive and time consuming. For me to make a single batch (3 quarts) it costs me about $20. But you also need a screen to get all the too tiny pieces out. Several gardeners on here use the mix and suggest Folliage Pro fertilizer with it. That it what I use as well and my plants are all very happy and healthy. If you want a cheaper mix just mix Cactus and Succulent soil with perlite. About half and half. That is at least better than regular potting soil and the Jade will be ok in that. But you'll still need to be careful of overwatering. With the gritty mix you won't have to worry.