My suggestion, starting today, go see a therapist who specializes in burnout and depression. There are a lot of them. They can help and will help you to enjoy and use your sabbatical. Go for it! Enjoy it! But please, seek out professional help.
Have you or someone you know well been helped through burnout by a therapist who specializes in burnout and depression?
Alternatively, have you or someone you know well tried unsuccessfully to get rid burnout on your / their own?
The problem was I did not believe in the therapy portion. I thought medication was easy. But it didn't work. One day I ended up into my physician and she said "either you go to a therapist or I'll lock you in my trunk and let you out when you'll go to a therapist." So, I went to a therapist and also a psychiatrist who helped with the medication side.
It was like night and day. We talked. We worked through things I had no idea I needed to work through. I was weened off of the medication. And I was given the power and principles needed to help me in the future. I cannot recommend it highly enough.