My understanding is that the costs around nuclear aren't due to the technology being expensive (something that yes, we would expect to get cheaper over time), but because of the -- IMO necessary -- regulatory and safety regime surrounding nuclear power. Costs that I wouldn't expect to change all that much (and maybe even increase with time).
With storage, the cost is mainly the technology. As the tech improves, the cost decreases.
However, I don't think the decline in battery prices is primarily due to the technologies used. Instead, it's more about economies of scale and demand, which help optimize prices.
From my perspective, nuclear energy is on a similar path but with significantly less investment. A major portion of nuclear costs stems from the lack of economies of scale.
In my opinion, the arguments against nuclear energy contribute to the perception of its economic inefficiency. If people don't believe in it or don't want it, there will never be an opportunity to achieve economies of scale.
Here its quite well documented: https://www.construction-physics.com/p/why-are-nuclear-power...