Yes, there is some investment in batteries, but due to how the market is structured, they are either equivalent of local large scale UPS, or mainly operate grid frequency stabilization while fossil fuel plants spin up or down (some of the "spin down" support can be also done with modern wind turbines, as they can operate as "sinks" on energy).
Unless we reset the way energy market operates in EU to prioritize dispatchable-but-fossil-free[1], I think we won't see neither proper nuclear resurgence, nor appropriate battery build up.
[1] My personal idea is that we should promote and prioritize sources that offer stable and dispatchable power without emissions. Such conditions would be fulfilled both by nuclear and renewables combined with energy storage, promoting build up of energy storage.
But as it is now, that's not something that is happening in EU, as far as I know. Some of the more recent projects turned out to have a tendency to go on fire.
As for USA, I have no idea how well it works out, as USA seems to have wildly different market setup than EU. My usual sources show under 1% for California.
It's also silly to use batteries as base load, as is the concept of base load in general in combination of cheap, but non-dispatchable, renwables, which is one of the things that hurts the economics of nuclear plants.
The only reason nuclear scales so slowly is because of the bureaucracy.
https://www.france24.com/en/france/20220825-france-prolongs-...
Taking down such reactors is a periodically routine for maintenance. The question is only how fast you can bring them up again (especially in case of serious repair needs).
That can be easily rectified by building energy conservation facilities for wind (and other renewables) instead of halting wind generators.
No, you cannot avoid using electricity few months in summer to have electricity for the rest time. And you cannot double the number of extremely costly NPs to have one half online while another half is being maintained/repaired.