Putting a man on the moon is a great technical achievement, but really, the reason people remember it so much is that it is a pissing contest that the US won. But being able to be productive against bureaucracy is maybe the greatest achievement for a big country. And I am sure that's also what made Apollo successful.
Operation Warp Speed probably won't feature in the history books, it is not as symbolic as a moon landing, it just made vaccines available a bit sooner. I don't think it really changed the course of history, but the time savings have saved thousands of lives, maybe millions, shortened lockdowns, allowed schools to open, etc... It is just statistics, but there are some statistics I am happy not to be part of.
1) Vaccine development in itself was no doubt a historical achievement and will go down in history books. Regardless of causality, Project Warp Speed will be there by association.
2) It is a meme that legitimizes government spending. "We need a project warp speed for FooBar" will be a powerful way to get things funded, in particular by republicans in the US, for many years to come.
If that's true, it's also a testament to how ossified bureaucratic boundaries have become.
It's like; America, 1969, "we put a man on the moon!". American, 2021, "we put a man into a position of authority outside of ordinary bureaucratic channels!". Maybe that's an achieve indeed but the context give one pause.