~99% of the cost is due to red-tape regulations. It's so obscene that they require certified backup genererators for the backup generators and 3-4 layers of fail safes. Then you need to wait YEARS to get all the permits and licenses. Oh and if you get preapproval for a componant (say the generators) but too much time has passed from installation until you actually are ready to go, you need to go through the process again, hence the constant delays. An actual nuclear power plant is actually stupidly cheap to run if you cut all the red tape. Stupidly. Like $50k of fuel produces $50 million of electricity good.
Edit because I forgot to mention this, if coal or ccgt were regulated like nuclear is, not a single one would be profitable. And even if you take into account every single death due to radiation poisoning (from any source) nuclear would still be the safest power source in the world. Literally worker deaths from installing wind power plants exceed it.
Nuclear power plants are ultimately not that different from coal power plants. Typical estimates for the capital costs of coal power are ~$4000/kW, which can be used as a lower bound for the costs of nuclear power.
The costs are high, because construction industry has suffered from poor productivity growth for decades. Renewables are getting cheaper, because they rely more on mass-produced stuff and less on hiring people to construct a big specialized building to house the power plant. Regulatory costs of nuclear power also largely come from poor quality control in construction industry. Regulators require something specific, subcontractors try doing that but often don't get it right, and regulators order them to tear it down and try again.