@Charred - You can make your own battery if you want. I did it for a science project way back in school. It’s a lot easier than you think.
All you need is one lemon, copper wire and a galvanized nail. You should also get hold of a volt meter to measure the electric current.
All you have to do is stick the copper wire and nail into the lemon (make sure they don’t touch each other), and that’s it, you have a battery.
Both the wire and the nail act as different poles of the cell. Use the volt meter to touch a probe to each pole, and you’ll read some minor electric current on the meter.
It’s super easy, and so yes, I think in that sense the Babylon battery may well have been what it looked like, a battery and not just a glorified vase.