I will try to answer this the best that I can, but I would argue that it is hard to take the New Deal and lump it all together. Two great books that tackle this are McElvaine’s Down and Out in the Great Depression: Letters for the Forgotten Man and his book simply titled The Great Depression. The former is a collection of letters written to the Roosevelts during the Depression and serves as, at least in my opinion, a template for the latter book’s creation. The New Deal is a less monolithic piece of legislature than it is often portrayed and talked about.

I don’t have my sources immediately available, but the first thing to do is to split the New Deal into two parts, the early parts roughly 1933-1935/36 and the latter parts 1937-1941. This is because Roosevelts second term brought about a shifting political landscape as the overwhelming majority the democrats had in the Federal Government slipped a little bit in the election of 1936. This was caused by a small recession that occurred in 1935-1936 ish if I remember correctly.

On top of this the New Deal was not just one monolithic piece legislature like 2009’s TARP or the current BBB bills. It was a combination of a lot of smaller bills and executive orders, with a fair number of both being shot down by the Supreme Court. It is why the New Deal is sometimes referred to as “Roosevelt’s Alphabet Soup.” You had the Agricultural Adjustment Act (AAA), The Emergency Conservation Work Act (ECW), and the National Industrial Recovery Act (NIRA). These acts also created a ton of varied and different agencies to oversee their portion of the New Deal, with my personal favorite being the Civilian Conservation Corps (CCC).

Additionally, we need to look at the two methods that you mentioned were used to help the economy recover, Hoover’s Austerity and Roosevelt’s Keynesian economic ideas. Hoover, and by extension the Republican Party, believed that by cutting government spending and having fiscally conservative policies the markets would eventually self-correct and everything would sort itself out. It placed an emphasis on the individual person being fiscally responsible and “tightening their belts.” Whereas Keynesian economics believes that when the economy enters a depression the government should open the flood gates of government spending and try to put money in the economy.

These are super oversimplified explanations of these policies, but they get us to the New Deal more to your question of did the New Deal actually do anything? Unsurprisingly the answer is complicated, because Yes some programs did help and No some did not. Something you yourself noticed in your question.

Overall, I do not think it is fair to look at the New Deal monolithically, each part is different. Individual parts helped in different ways and others did not. The CCC for example, Neil Maher cites this agency as having a roughly 80% approval rating in his book Nature’s New Deal. He also goes on to argue that the program put young men with little to no experience to work improving the country’s farmland, National Forests, and National Parks. There is a wealth of material championing the CCC, including myself. This goes back to the fact that in many ways you need to look at it piecemeal.

McElvaine ends his book with a similar stance if I recall, but I think he would agree that overall, I think it’s fair to say that the New Deal was a mixed bag policy that did not go far enough. Much like the criticisms of those modern-day policies from the 2007-8 recession. It definitely stabilized the economy for the most part and led to the US being able to tool up for the Second World War much faster. I think the best way to categorize the New Deal is that it stopped the bleeding, and helped to stabilize the economy, for the most part, but failed to go much beyond that.

Hopefully this makes sense and is not just the ramblings of a madman.