How can I add hatches, stripes or another pattern or texture to a barplot in ggplot?

One approach is to use the ggpattern package written by Mike FC (no affiliation):

library(ggplot2)
#remotes::install_github("coolbutuseless/ggpattern")
library(ggpattern)
ggplot(data = df, aes(x = Class, fill = StudyTime, pattern = Nerd)) +
  geom_bar_pattern(position = position_dodge(preserve = "single"),
                   color = "black", 
                   pattern_fill = "black",
                   pattern_angle = 45,
                   pattern_density = 0.1,
                   pattern_spacing = 0.025,
                   pattern_key_scale_factor = 0.6) + 
  scale_fill_manual(values = colorRampPalette(c("#0066CC","#FFFFFF","#FF8C00"))(4)) +
  scale_pattern_manual(values = c(Nerd = "stripe", NotNerd = "none")) +
  labs(x = "Class", y = "Number of Students", pattern = "Nerd?") + 
  guides(pattern = guide_legend(override.aes = list(fill = "white")),
         fill = guide_legend(override.aes = list(pattern = "none")))

The package appears to support a number of common geometries. Here is an example of using geom_tile to combine a continuous variable with a categorical variable:

set.seed(40)
df2 <- data.frame(Row = rep(1:9,times=9), Column = rep(1:9,each=9),
                   Evaporation = runif(81,50,100),
                   TreeCover = sample(c("Yes", "No"), 81, prob = c(0.3,0.7), replace = TRUE))

ggplot(data=df2, aes(x=as.factor(Row), y=as.factor(Column),
                     pattern = TreeCover, fill= Evaporation)) +
  geom_tile_pattern(pattern_color = NA,
                    pattern_fill = "black",
                    pattern_angle = 45,
                    pattern_density = 0.5,
                    pattern_spacing = 0.025,
                    pattern_key_scale_factor = 1) +
  scale_pattern_manual(values = c(Yes = "circle", No = "none")) +
  scale_fill_gradient(low="#0066CC", high="#FF8C00") +
  coord_equal() + 
  labs(x = "Row",y = "Column") + 
  guides(pattern = guide_legend(override.aes = list(fill = "white")))