R, ggplot, combine 10 variables into one bar graph

I have data that I've extracted from a site called "Redcap", the data looks like this on REDCap:

I.e. it was one "question" that respondents could pick multiple answers for, but they all got graphed together. To reiterate, the answers were NOT mutually exclusive.

Here's a sample of the de-identified data:

df<-structure(list(improvement___1 = c(1, 0, 1, 1, 1, 1, 1, 1, 0, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), improvement___2 = c(0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 
0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 1), improvement___3 = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 
1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), improvement___4 = c(1, 
0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 
1, 1, 1), improvement___5 = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0), improvement___6 = c(0, 
1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 
0, 1, 1), improvement___7 = c(0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 
0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 
1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0), improvement___8 = c(0, 
1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 
0, 1, 1), improvement___9 = c(1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 
1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1), improvement___10 = c(0, 
0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0), AgeGroups = structure(c(2L, 1L, 2L, 1L, 2L, 1L, 3L, 
1L, 2L, 2L, 3L, 2L, 2L, 2L, 2L, 3L, 2L, 2L, 3L, 1L, 2L, 2L, 1L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 3L, 3L, 2L, 2L, 3L, 2L, 2L, 3L, 
3L, 1L, 2L, 3L, 1L, 2L, 1L), .Label = c("Young", "Middle", "Old"
), class = "factor")), row.names = c(NA, -46L), class = c("tbl_df", 
"tbl", "data.frame"))

Because respondents could pick multiple answers, each answer is really its own variable and when exported, I get a column for each (Improvment_1 is the first row, improvement_2 the second, etc..). I'd like to create a graph, almost identical to the one I pasted, but faceted by the other variable I included: "AgeGroup". So it'd look like this (pardon my msPaint skills):

I'm struggling with how I would include 10 different "improvement" variables on the same graph.

I admire your MS paint skills. Is this what you are looking for?

library(tidyverse)
df_new <- df %>% 
  pivot_longer(-AgeGroups, "improvement")

ggplot(df_new) +
  aes(x = improvement, weight = value) +
  geom_bar(fill = "#112446") +
  coord_flip() +
  theme_minimal() +
  facet_wrap(vars(AgeGroups))