Initially I thought this was some kind of mechanical regenerative braking. I wonder if that's been attempted before.

Applying the brakes would wind a spring and bring the bike to a stop. Then applying force to the pedals or manually pulling a lever would release the spring for an assisted start.

Edit: Here's some mechanical regenerative braking projects:

https://m.youtube.com/watch?v=yK7fyugbe6o

https://m.youtube.com/watch?v=DoaJK39Tl60

Electrical regen is probably cheaper and lighter.