Pumped storage needs a lot of water to start but can then just cycle the water between reservoirs. Some will be lost by evaporation, but that loss isn't that high.

I once compared a proposed pumped hydro system in Arizona near Phoenix vs. the water evaporated by the Palos Verde nuclear generating station. Per unit of levelized power output, the pumped hydro system used at least an order of magnitude less water than the nuclear plant.

That analysis ignores the prospect of siting a solar array floating on the reservoir, with benefits of reduced evaporation and cooler, more efficient conversion, an opportunity unlikely to be long neglected.

I'm not sure how practical floating solar would be on pumped hydro reservoirs. The water will go up and down a lot.

It will mostly only go down, anyway, when the sun is not out.

If the panels don't mind settling on the banks, or if they are far enough offshore not to, that will not be a problem. It is already common to float panels on regular hydroelectric generation reservoirs, so the event is anyway familiar to operators.

If the floats are bottom-heavy and attached to cables spanning the reservoir, the water dropping out from under just leaves them suspended. You need cable attachments, anyway, to extract power and maintain spacing.