This isn't my field, but I have read a few papers about the question of how profitable slavery was. Most of the debate seems to be over how profitable it was to the plantation owners, and whether they personally would have made larger profits by investing their money elsewhere (e.g., by hiring wage laborers to work their plantations, or by investing in manufacturing).
The question of slavery's impact on the development of the economy as a whole is completely different from that. Given how backwards the South remained, while the half of the country that abolished slavery surged ahead economically, it's difficult to see how one could argue that slavery caused the US' economic development.
Alexis de Tocqueville wrote about this in Democracy in America. It's well worth reading, to see a contemporary Frenchman's impressions of the stark difference in economic development between the Southern slave and Northern free societies: https://www.tota.world/article/1860/