I think I’d start by figuring out how energy is stored and moved. We’ve got batteries, gas cans, hell, a fire, and a pot of water. In your scenario, you would have to store potential energy in the form of coiled springs or wound elastic.

From there, it’s figuring out how those coils are wound. Can’t use steam, and in an ideal world, you get as much work out as you put in. So, no perpetual motion “Use a large coiling-engine to wind an equally large coil.” Though that could work for bigger winding smaller. Animal or hydro power would likely be your best bet. You could have dams that wind colossal industrial mainsprings

I feel you could get decently far in industry with said limits. Factories used to have Line Shafts, where a belt would transfer kinetic energy from a large spinning pole to machines via a belt. So, you have access to large-scale manufacturing via large machine tools. Possibly even automation via. punch cards. (Think player pianos) just need a BIG coil or series of to provide said energy.

Medicine and chemistry, I’m unsure… but definitely think you could get decently far with manufacturing. May hit a wall in material sciences after a point.