Thank you all for your advice! I was worried that the fall would be automatically fatal, so I'm really glad to hear that it can be survived.
Sweet Boy remained at the base of the tree for around 10 minutes before he attempted to climb it again. He made it this time, thankfully! Since then he has been laying on one of his favorite branches like he usually does in the afternoons.
Sweet Boy's back legs/feet don't seem to move as well as they should but I have no idea what the problem is. Here is a video of him climbing a different tree just a few days ago.
https://youtu.be/GQawzTI9dRo