How to plot p-values in a circular barplot?
The adjustcolor function from grDevices can be used to generate colours with transparency. What you want is colours based on the pathway and transparency to form a colour gradient for the p-value.

adjustcolor( "red", alpha.f = 0.2)

For the ggplot example, the aes function has an alpha parameter.

ggplot(df2, aes(x = factor(Pathway_names), y = Entities_found), alpha = Entities_pValue) + ######################################
geom_bar(aes(fill = Entities_found, alpha = Entities_pValue), stat = "identity", position = "stack") +  
coord_polar() + 
theme_minimal() + 
 guides(fill = FALSE)