The New Deal was primarily a jobs program, not a rise in worker protection, and the things that pass for worker protection are really quite anti-progressive or subtle covers for various corruption.
For example, social security pays benefits based on past income rather than a fixed or need-based payment, and the social security tax is a flat rate with an income cap, making it one of the most regressive taxes short of a poll tax. Meanwhile the amount of political corruption and mafia involvement in labor unions in the era of the Wagner Act makes it highly suspicious that their original purpose or effect was actually labor protection.
And to the extent that there were new actual labor laws, they were often largely symbolic or ineffectual. For example, the original federal minimum wage only applied to jobs in interstate commerce, which at the time actually meant interstate commerce. By contrast, many of the actually-meaningful state-level minimum wage laws were passed during the boom times in the 1920s.
Most of the meaningful labor and safety regulations we have came out of the economically prosperous period of the 1950s and 60s, e.g. that's when the federal minimum wage was extended to other workers, and then extended further in the economically prosperous period in the 1990s.