Remember that energy and power are distinct quantities. A battery can easily match the power output of pumped hydro, but pumped hydro can exceed the energy storage of even the largest battery. The energy storage of pumped hydro is only limited by the size of the lakes, and lake size is only loosely linked to cost since the lake will potentially already exist. If a lake is artificial, volume increases non-linearly as a dam gets higher.
For example, the largest batteries can currently store about 3GWh of energy, but Snowy 2.0 will store abut 350GWh. Smaller pumped hydro schemes are typically 8GWh up.
Pumped hydro is suited for wind storage, and lithium ion is suited for solar storage, is a good approximation.
Snowy 2.0 with 2.2GW power and 350GWh energy will be great for multi-day wind surplus followed by multi-day dunkelflaute. But not as useful for solar, which is more stable, and where the droughts are seasonal in nature rather than weekly.
For example, the largest batteries can currently store about 3GWh of energy, but Snowy 2.0 will store abut 350GWh. Smaller pumped hydro schemes are typically 8GWh up.