At first glance, this seems to a be a Rosenwald School, but it doesn’t have the hallmark bays of windows. There are Rosenwald Schools that deviate from Rosenwald plans, and there are many schools that used the plans because of their efficient designs.
I agree with the assessments made by Random Connections and the South Carolina Picture Project. Shiloh Baptist Church does share the property with the school. The oral history of any older church members would be needed to verify.
The Rosenwald database is currently down and is anticipated to return in the Summer of 2023. While the site is being revamped, it may not have additional info. I did search some out-of-print books on South Carolina education and Rosenwald schools and found nothing.