You mis-copied the numbers for one launch. Wiki says:

> Project cost US$6.417 billion (equivalent to $33.6 billion in 2023)

> Cost per launch US$185 million (equivalent to $969 million in 2023)

That a manned Apollo mission would/did cost under a billion dollars (todays money) is surprisingly cheap. A single Artemis launch using the Space Launch System (SLS) costs an eye watering $4 billions.

Different metric:

> [1966] NASA received its largest total budget of $4.5 billion, about 0.5 percent of the gross domestic product (GDP) of the United States at that time.

Using that metric NASA yearly budget would with todays GDP be $150 billion dollars.

Part of the SLS cost comes from trying to save money. Yearly budgets are kept low, which spreads out the work over a long time. This makes everything cost more, but the politicians only care about the yearly spending.

SLS is also a pretty weird design due to reusing Shuttle components for a completely different kind of launcher. This saves development costs (maybe) by using existing stuff that has already been developed, but the unsuitability of those components for this system increases per-launch costs. Once NASA runs out of old Shuttle engines, manufacturing new ones is going to cost $100 million apiece if not more, and each launch needs four of them. It was OK for Shuttle engines to be expensive since they were supposed to be amortized over hundreds of flights (and in practice were actually amortized across at least tens of flights) but now they’re being used in expendable launches. If Starship even comes remotely close to its goals, an entire launch will cost less than a single SLS engine.

Some of this was the overall urgency of the 1960s space race, that people were motivated to cut through red tape and get it done, and I know it's also argued that modern safety standards and requirements around supply chain, real time monitoring, system redundancy, etc all complicate things and raise costs.

That said, it would be interesting to have someone really knowledgeable go over what it is that Artemis has and Saturn V didn't, and then break them down and assign each an approximate proportion of the cost delta.

In recent years, NASA’s budget has hovered around $25–27 billion.

This represents less than 0.5% of the total U.S. federal budget, though it’s one of the most visible and impactful science agencies

facepalm not sure how I misread that