If you want to include the options to download the current page and the entire dataset as both a csv or an excel file, I've managed to implement this as two separate dropdown buttons with those options, together with the copy and print buttons:

Here is the modified working code:
library(shiny)
ui <- fluidPage(
DT::dataTableOutput("table")
)
server <- function(input, output, session) {
output$table <- DT::renderDataTable(server = FALSE, {
DT::datatable(
mtcars,
extensions = "Buttons",
filter = "top",
selection = "none", #this is to avoid select rows if you click on the rows
rownames = FALSE,
options = list(
scrollX = TRUE,
autoWidth = FALSE,
dom = 'Blrtip', # the important thing is that there is the l to allow for the lengthMenu
# https://stackoverflow.com/questions/52645959/r-datatables-do-not-display-buttons-and-length-menu-simultaneously
buttons = list(
# insert buttons with copy and print
# colvis includes the button to select and view only certain columns in the output table
# from https://rstudio.github.io/DT/extensions.html
I('colvis'), 'copy', 'print',
# code for the first dropdown download button
# this will download only the current page only (depends on the number of rows selected in the lengthMenu)
# using modifier = list(page = "current")
# only the columns visible will be downloaded using the columns:":visible" option from:
# https://stackoverflow.com/questions/72317260/how-to-download-only-the-selected-columns-in-a-dataframe-using-colvis-from-dt-in/72317607#72317607
list(
extend = 'collection',
buttons = list(
list(extend = "csv", filename = "page",exportOptions = list(
columns = ":visible",modifier = list(page = "current"))
),
list(extend = 'excel', filename = "page", title = NULL,
exportOptions = list(columns = ":visible",modifier = list(page = "current")))),
text = 'Download current page'),
# code for the second dropdown download button
# this will download the entire dataset using modifier = list(page = "all")
list(
extend = 'collection',
buttons = list(
list(extend = "csv", filename = "data",exportOptions = list(
columns = ":visible",modifier = list(page = "all"))
),
list(extend = 'excel', filename = "data", title = NULL,
exportOptions = list(columns = ":visible",modifier = list(page = "all")))),
text = 'Download all data')
),
# add the option to display more rows as a length menu
lengthMenu = list(c(10, 30, 50, -1),
c('10', '30', '50', 'All'))
),
class = "display"
)
})
}
shinyApp(ui, server)