How to use map_at properly in a nested list?

I have a nested list of lists that include data tables at the bottom level. My goal is to map a function to a single table to transform the data. I'm currently trying to use purrr:map_depth and purrr::map_at in conjunction to create the plot. The reason I need to use map_at or map_if is the plot function I'm using takes different arguments depending on the table.

example below

library(data.table)
library(purrr)

example = list(
  group1 = list(
    all = data.table(
      x = 1:10,
      y = 10:1),
    not_all = data.table(
      x2 = 11:20,
      y2 = 20:11)
    ),
  group2 = list(
    all = data.table(
      x = 1:10,
      y = 10:1),
    not_all = data.table(
      x2 = 11:20,
      y2 = 20:11)
  ),
  group3 = list(
    all = data.table(
      x = 1:10,
      y = 10:1),
    not_all = data.table(
      x2 = 11:20,
      y2 = 20:11)
  ),
  group4 = list(
    all = data.table(
      x = 1:10,
      y = 10:1),
    not_all = data.table(
      x2 = 11:20,
      y2 = 20:11)
  )
)

I'm planning to use highcharter::data_to_boxplot as the mapping function.

So far I've been unable to extract a single table to map to and don't have a solid grasp of the purrr syntax yet.

map_depth(example, 2, map_at(., "all", data_to_boxplot, variable = x))
# Error: character indexing requires a named object

map_depth(example, 2, ~map_at(., "all", data_to_boxplot, variable = x))
# this prints out the entire list

# would like to try something like this too but can't figure out the piping correctly
map_depth(example, 2) %>%
  map_at(., "all", data_to_boxplot, variable = x)

# Error in as_mapper(.f, ...) : argument ".f" is missing, with no default

Any help would be greatly appreciated!