I wouldn't be too panicked about the roots because Jade plants can grow new roots even from a single leaf. All you need to do is make sure it gets the conditions it needs to be strong enough to grow new roots.

What were you planning to repot it in? The goal for most plants, but especially succulents like Jade, should be to give them a potting mix that drains well so the roots can receive ample oxygen.

Do you have a sunny location for it? If it can get a lot of bright light, that will help it grow much more strong and compact.

If the roots are rotted, I would make sure to cut them off

The pictures indicate that your jade was in a soil that is far too wet and doesn't drain well. That's a very weak root system. It also appears that your jade wasn't getting nearly enough light, as the growth is thin and spindly, with long internodes. You'll want to look into a faster draining mix, such as "gritty mix", and give your jade as much light as you can. Outdoor sun during the warm months really gets them growing strong, but be sure you acclimate them slowly to direct sun.

Joe