I mean this is where pumped hydro would be pretty handy actually. Pumped hydro can't charge as fast as batteries, but can have enormous energy capacity.
You could almost certainly tune a pumped hydro installation to absorb the ramp of a reactor cycling up and down, but you'd lose the risk of running dry due to renewable unpredictability.
Most places where pumped hydro is viable already have it. The growth potential is limited.
Hydrogen is a more interesting option. Not necessarily for energy storage, but as a fuel for use cases where electricity can't be used (like fertilizer or methanol rather than cars or heating).
Pumped hydro can store more energy then any battery array. You can size a battery, or pumped hydro, to any power level you like, but batteries by their nature scale differently: the faceplate capacity of a battery multiplied by 4 is also pretty much the energy storage.
Whereas pumped hydro can store far more energy (limited by upper reservoir size) then any battery array, but you pay for it in the fact that if you have a 1 MW turbine system on it, and 100 MWh of storage, you still only have 1 MW of power capacity (and about 100 hours of storage).
The problem is 100 hours of storage isn't much use if your grid needs more then that right now and it also can usually only be "charged" at about half that rate, so that 100 hours takes 200 hours to accumulate and that number is fixed - there's no surge capability - but if you're dealing with solar panels putting out on average 30% of their faceplate power, but obviously peaking at 100% frequently, you need to be able to store the peak to store it at all.
You said "Pumped hydro can't charge as fast as batteries".
This simply isn't true, there are dozens of pumped storage plants that can store energy faster than any grid battery that has been constructed to date. If you meant that the typical battery reaches capacity faster, that's not really a feature, it's a limitation.
You could almost certainly tune a pumped hydro installation to absorb the ramp of a reactor cycling up and down, but you'd lose the risk of running dry due to renewable unpredictability.