dplyr - Need to add the CSV filename after importing all files from a directory

I have used this code to import all csv files from a directory

orgs <-
  list.files(pattern = "\\.csv$") %>% 
  map_df(~read_csv(., col_types = cols(.default = "c")))

Which has successfully combined all files in the directory into one data frame

I am looking for a way to add the file names of the csv files imported as an addtional variable

Looking something like

Something like this?

lapply(list.files(pattern = "\\.csv$"), \(x) {
  read_csv(x, col_types = cols(.default = "c")) |>
  mutate(Filename=x)  }) |>
  bind_rows()

Returns (for the data generated below):

   Sepal.Length Sepal.Width Petal.Length Petal.Width Species Filename 
   <chr>        <chr>       <chr>        <chr>       <chr>   <chr>    
 1 5.1          3.5         1.4          0.2         setosa  iris1.csv
 2 4.9          3           1.4          0.2         setosa  iris1.csv
 3 4.7          3.2         1.3          0.2         setosa  iris1.csv
 4 4.6          3.1         1.5          0.2         setosa  iris1.csv
 5 5            3.6         1.4          0.2         setosa  iris1.csv
 6 5.4          3.9         1.7          0.4         setosa  iris2.csv
 7 4.6          3.4         1.4          0.3         setosa  iris2.csv
 8 5            3.4         1.5          0.2         setosa  iris2.csv
 9 4.4          2.9         1.4          0.2         setosa  iris2.csv
10 4.9          3.1         1.5          0.1         setosa  iris2.csv

Note that map_df was superseded in purrr 1.0.0.

Data:

library(dplyr)
library(readr)

write.csv(iris[1:5,], "iris1.csv", row.names=FALSE)
write.csv(iris[6:10,], "iris2.csv", row.names=FALSE)