You can't figure out what to do during your sabbatical, because you're burned out and completely unmotivated and you won't be able to find it out until it changes. So the solution is to do nothing 'meaningful' for a while. Don't think about projects, PhD, start ups or anything. Just take a break and do nothing tat resembles work.
Starting wit traveling is a very good option. This is also what I did. Go to a totally different place. A different (non-western) culture. Not to help or work, just to be there. A lot of people go to South-East Asia. I did that too and loved it. My thinking and problems were reduced to what to eat, where to eat, where to sleep and what to see next.
You can do this for months. Then you may start to miss your work, you may start to have ideas again. You'll probably miss thinking and you will find out what to do during the rest of the leave.
Starting wit traveling is a very good option. This is also what I did. Go to a totally different place. A different (non-western) culture. Not to help or work, just to be there. A lot of people go to South-East Asia. I did that too and loved it. My thinking and problems were reduced to what to eat, where to eat, where to sleep and what to see next.
You can do this for months. Then you may start to miss your work, you may start to have ideas again. You'll probably miss thinking and you will find out what to do during the rest of the leave.