I agree with Sylvain. But do what you are comfortable with.
Great caudex/roots! The bit that is drying could be OK, keep an eye on it. Don't be in a rush to repot. I've had plants bare root for months and months. Haha, ask Wilfred, I sent him some yearlings that hadn't seen soil or water for something like five or six months.
I think I would cut the mushy branch just above the joint, not trying to get all the soft part. These plants really can heal themselves.
Don't worry if a few leaves drop off. Or they might not! I won't be back online until Monday late...
crazy plants.
