Why exactly has it gotten more expensive?

I see two reasons:

Increased nuclear safety. Proponents often tout nuclear's relative safety. Good, but that safety is hard won through regulation. Compliance is costly, and improved safety has been subject to diminishing returns.

Economies of scale. Building a nuclear power plant is a massive undertaking, so the world simply hasn't been building a lot of nuclear power plants. Supply chains (parts, know how) are getting smaller and more uncompetitive with every passing year as other forms of energy production have become more attractive.

In large part, because civil engineering projects got more expensive.

I dont really know why civil engineer projects of all kinds have gotten so expensive but they have. One would think that the more we learn from our failiures the more things we have to make sure we do right and that should take more time, on the other hand we should also learn to streamline and use technology to speed things up, but apparently not enough.

It could be an example of Baumol's Cost Disease.

https://en.wikipedia.org/wiki/Baumol%27s_cost_disease

Because otherwise even a state wouldn't want to vouch for it.