With pumped storage you don't need anywhere near the amount of water or storage needed for straight Hydro. In a 24 hour cycle, you can empty the top dam into the low dam, running the generators flat chat (unlike typical hydro which is limited by water supply), then pump it back up again for reuse. If you do the numbers (E=m.g.h) the amount of water required to store energy for a city of millions is quite tractable, assuming a decent head.

Australia is doing exactly this with "Snowy 2.0" (by connecting existing dams).

https://www.snowyhydro.com.au/snowy-20/about/

350,000 megawatt hours of energy storage, which is enough to power 3 million homes for a week, or (if there was enough generation/transmission capacity to get the energy in/out fast enough) the entire nation for 12 hours.