geom_bar - stack + dodge for categorical variable

I did find something about this for numeric values (ggplot bar chart with two dataframes) as well as date, but not for categorical, so I'm having issues.

I would like "grade" to be the stack, and then have the two groups next to each other at each x-axis point.

library(ggplot2)
data <- data.frame('group'=c(rep('g1',50), rep('g2',50)), 
                   'grade'=c(rep('1-2',20), rep('3-4',40), 
                             rep('1-2',35), rep('3-4',5)),
                   'problem'=c(rep('p1',5), rep('p2',52), 
                               rep('p3',29), rep('p4',14)))

This is what I'm using to just do the grade part, with descending frequency

ggplot(data, aes(fill=grade, x=reorder(problem, problem, 
       function(x)-length(x)))) + 
  geom_bar(aes(y = (..count..)/sum(..count..)))

I tried this based on the link provided, but it doesn't work because problem isn't numeric

ggplot(mapping=aes(x=problem)) +
  geom_bar(data=data1, aes(x=problem-0.1), fill="red", binwidth=0.1) +
  geom_bar(data=data2, fill="blue", binwidth=0.1)

Should I just map problem to numeric, and then relabel it, or is there a way to do an offset for a category? There was also an example using dates (geom_bar(): stacked and dodged combined) where the shift works, presumably because dates have numeric equivalents.

I shuffled the group column to showcase the solution better; here's the plot for the original data.

library(ggplot2)

set.seed(42)
data <- data.frame(group = sample(c(rep('g1', 50), rep('g2', 50))), 
                   grade = c(rep('1-2', 20), rep('3-4', 40), 
                             rep('1-2', 35), rep('3-4', 5)),
                   problem = c(rep('p1', 5), rep('p2', 52), 
                               rep('p3', 29), rep('p4', 14)))

within(data, 
       xdoge <- as.integer(reorder(problem, problem, 
                                   function(x) -length(x))) + 
         0.4 * scale(as.numeric(as.factor(group)), scale = FALSE)) |> 
ggplot(aes(x = xdoge)) + 
  geom_bar(aes(color = group, y = after_stat(count)/sum(after_stat(count))), 
           width = 0.35, size = 2, fill = NA) +
  geom_bar(aes(fill = grade, y = after_stat(count)/sum(after_stat(count))), 
           width = 0.35) +
  scale_x_continuous(breaks = seq_along(unique(data$problem)),
                     labels = levels(reorder(data$problem, data$problem, 
                                             function(x) -length(x)))) +
  scale_colour_grey(start = 0.4, end = 0.8) +
  theme_bw() +
  labs(x = "Problem", y = "Proportion",
       fill = "Grade", color = "Group")

_{Note that dot-dot notation is deprecated. Use after_stat.}

^{Created on 2025-07-25 with reprex v2.1.1}