Will desert rose regenerate new branches after losing all old ones?
Caudex is still healthy & firm. In this condition at least 4 months.
I have seen these recover from near death many more times than I can count. Giving them proper care will, likely, let it recover just fine.
This article will help with the proper care of these: https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/caring-for-desert-rose-plants.htm