What we are seeing now is that more and more households with solar are also installing batteries. About 80% of all grid battery storage is now in private households (at least in Germany)... and that's just the part we have data from, many households are probably just to lazy to register their batteries.
Those households then will store their self-harvested energy in the batteries, using it, particulary, when dynamic electricity prices are high, thus lowering the demand at times when supply is low.
Commercial battery storage is mostly held back by the government with their pro-fossil agenda, but we'll likely see more storage at power plants and consumers like office buildings, also stabilizing the grid. In fact there are calls to demand a bit of storage on every big plant, so that they can momentarily (for seconds) feed in more power. This is supposed to emulate the "rotating masses" phenomenon of classical power plants.
Probably the main problem today are right-wing governments (at least in Germany) who, increasingly, want this all to fail, sabotaging it where ever they can.