How did national, political, and economic factors influence the outcome of the "Scottsboro Boys" legal case, and how did this incident influence the politics and race relations of the 1930s?

The 1931 "Scottsboro Boys" case—in which nine African American males, including minors as young as 12, were tried and falsely convicted (the 12-year-old was the only defendant acquitted) of raping two white women—occurred squarely in the context of the continued racial animosities and endemic poverty of the American South. Every individual involved, from the accused to the accusers, were desperately poor and mostly uneducated. The racism that dominated Southern culture in the antebellum and post–Civil War eras remained very much a part of the local culture in Alabama, as elsewhere in the region, and institutionalized segregation was the law of the land. As importantly, there was no issue more inflammatory in that place and time than the accusation of the rape of white women.
While the American South had remained an extremely polarized environment with respect to race relations, the US as a whole had been gradually—very gradually—moving in the direction of addressing the problem of systemic racism in society. It would be two to three more decades before landmark Supreme Court decisions and legislative initiatives, especially the 1954 Brown v. Board of Education decision and the Civil Rights Act of 1964, were finalized, but consciousness of the immorality of racism was growing in many parts of the country. This, then, was the environment in which the "Scottsboro Boys" case transpired. That it would undergo repeated retrials and appeals was a significant measure of the country's progress, slow and flawed as it was.
The "Scottsboro Boys" case remains a defining moment in American jurisprudence for the miscarriage of justice it represents. That most of the defendants were initially sentenced to death, an obviously irreversible and particularly draconian penalty, was especially troubling given the complete absence of evidence indicating that any crime perpetrated by the African Americans had occurred. One of the two white women would eventually concede the obvious, that no rape had occurred, but the accusation was sufficient to put into motion a chain of events that unjustly ruined the lives of those falsely accused. The endemic poverty, lack of adequate education, and virulent racism evident in the case’s history were all contributing factors, but the latter was the most disappointing given the turmoil of the nation’s past and the failure of Reconstruction to adequately transform a regional culture that discriminated harshly against those of African heritage. That much of the country was following the proceedings (at least via newspapers and radio), however, was instrumental in keeping the legal system attentive to such an obvious travesty. Absent that attention, one could logically conclude that those death sentences would have been carried out. Only because of that attention from outside of the American South did the US Supreme Court overturn the conviction in Powell v. State of Alabama and spare the lives of those falsely accused. Subsequent Supreme Court decisions would serve to lessen the likelihood of the initial trial's outcome by mandating that juries (the defendants were tried by all-white juries) must better represent the communities in which the alleged crime occurred.
https://nmaahc.si.edu/blog/scottsboro-boys

https://socialwelfare.library.vcu.edu/eras/great-depression/scottsboro-boys-trial-defense-campaign-1931-1937/

https://www.pbs.org/wgbh/americanexperience/features/scottsboro-boys-who-were-the-boys/