Just a note — crediting New Mexico with the entire Manhattan Project is no more justified than crediting Washington State, or California, or Tennessee, with it. Many states made huge contributions to the project. The New Mexico component was substantial, but it is not necessarily "important" in the sense that if it had not taken place in New Mexico, it wouldn't have taken place elsewhere. There had been alternative sites considered for Los Alamos, there were even alternative sites considered for the Trinity test. New Mexico was largely chosen for its role in the Manhattan Project because Robert Oppenheimer had been there several times and liked it.

So there are a few things to break down here. First with the Manhattan project it is impossible to uncouple it from the economy. The cost of the Nuclear project was on par with the cost of all small arms material not including ammunition by the US in WW2. Such a program is incredibly challenging to undertake without a strong economy. Also timing is important. By the time the fruits of the Manhattan project were deployed the war in Europe had been won and the outcome of the war in the pacific was no longer in doubt. The All that was left was a question of how long the war would go on and how its length would affect the post war geopolitics as well as total casualties. As far as casualties u/restricteddata put together a pretty complete answer here https://www.reddit.com/r/AskHistorians/comments/q6cmsw/the_estimated_american_casualties_for_the/.

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That leaves the code talkers which is a lot harder to quantify. Would the lack of code talkers have meant the US and allies lost WW2? Highly unlikely. There were only around 400 code talkers by the end of the war so many messages were still transmitted in other codes and languages yet operations without the code talkers still managed to succeed in their objectives. Yet the personnel anecdotes of those who served with them were very flattering of the code talkers. The signal officer of the 5th Marine division was quoted saying “Were it not for the Navajos, the Marines would never have taken Iwo Jima.” Of course you have to take into account that this is an individual whos primary mission and focus is around communications and keeping them secure so his view of the code talkers is going to be influenced by that.

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So long story short, yes the economy was most likely more important then the code talkers and was for sure both essential to and overall more important then the Manhattan project.