Give colVis button an InputValue

On my datatable I use the Buttons extension for the colVisGroup functions to hide or show selections of columns.
This works absolut fine and as I aspect.

The I read that one can give buttons an Input Value via

action=DT::JS("function ( e, dt, node, config ) { Shiny.setInputValue('colvis_Input', true, {priority: 'event'});}"

to let observeEvent find them.

This also works absolut fine on my action buttons.

Now I want to combine these two and give every "Column Selection" an InputValue, but I can't get it to work.

I noticed that the action entry will "overwrite" the hide and show entries and when I assign an input value to a selection, it will not select these columns.

Is there a different way to assign the colvisGroup with an InputValue?
Is there a way to define the show and hide properties within the action?

Example Code:

server = function(input, output){
  
  colVis.button  = list(list(extend="colvis",text="Columns",columns=1:11,
                             prefixButtons=list(list(extend="colvisGroup",text="Selection",show=c(1,2),hide=3:11),
                                                list(extend="colvisGroup",text="Selection and Input value",
                                                     show=c(1,2),hide=3:11, 
                                                     action=DT::JS("function ( e, dt, node, config ) {
                                                         Shiny.setInputValue('colvis_Input', true, {priority: 'event'});
                                                         }"
                                                ))) ) )
  
  table = DT::renderDataTable(DT::datatable(mtcars,
                                              extensions = c("Buttons"),
                                              options=list(dom = "<t>B",buttons = colVis.button)))
  
  output$table = table
  
  shiny::observeEvent(input$colvis_Input, {
    print("colvis_Input")
  })

}
shiny::shinyApp(shiny::mainPanel(DT::dataTableOutput("table")),server)