Steel usage is on the order of 100,000t for a GW of nuclear reactor and a decent chunk is rebar rather than low alloy stainless. If we take it on the high end, that's about $200 million. Double it for finance costs and you're around half a billion. Stainless and heavy fabrication costs more, but that's not 'steel costs' per se.

Over its lifetime a NPP including fuel and upkeep is on the order of 20 billion/GW.

Might call it 5-10% at a stretch. Certainly not enough to double it. And if nuscale reactors are claiming to be much cheaper and less resource intensive then they're either lying about the steel costs being the cause, lying about hidden subsidies, or lying about using an order of magnitude more steel. Either way you probably don't want scam artists in charge of enriched uranium.

This is why we need to move away from pressurized water based reactors. Most of this material is in the shielding needed because the system is designed around keeping water at several hundred atmospheres pressure. Operating at atmospheric should dramatically reduce materials costs going forward (but still needs substantial research investment to get going and regulators that aren't so stuck in their ways)