In fact, it is not possible to produce electricity.
What you added only increased the electrolyte, which means the internal resistance of the battery is reduced and the conductivity is increased. This old battery seems to have power again when used, as you feel that little light. The light bulb lights up or the little toy can move again.
The principle of the battery is actually a redox reaction. Electrons are transferred through the graphite rod in the middle (general dry cell), so there is electricity. Salt water and urea do not undergo redox reactions and therefore cannot produce electricity on their own.
For larger batteries, like car batteries, you sometimes go to a service shop to add water or something like that. Actually, it's not water, but sulfuric acid or something.
You can boil or evaporate the water and the salt will leave a solid behind. If you want to collect water, you can use distillation. One way to do this at home would be to boil salted water in a covered pot. Shift the lid slightly so that the water on the bottom of the lid condenses into a separate container. Congratulations, you have just distilled the water. When all the water has boiled, the salt will remain in the pan. Evaporation works the same way, but at a slower rate