I had a bit of a tough time towards the end of my last job, and felt a similar ennui. If you can, I’d highly highly recommend picking up a completely unrelated hobby to fill your non work (and occasionally work, when you’re in that limbo) time. I couldn’t believe the effect it had on me, and it meant that I started my new role feeling refreshed and optimistic, rather than just diving into it like I normally do.
Personally, I hit the gym for 4 months, mostly to fix the lack of sleep that came with the restlessness and lack of mental exercise.