how to set shiny outputs from inside the function when using callr::r_bg

Question

I have a function which sets some output in a shiny app upon a click of a button. Since this process takes some time I want to run it in background. I really like callr package for this but I am facing some trouble implementing this in my current scenario.

I have created a small example to demonstrate my issue. First, an example which works without callr.

library(shiny)

ui <- fluidPage(
  actionButton("click", "click me!"),
  textOutput("text")
)

server <- function(input, output, session) {
  
  call_fun <- function(input, output) {
    Sys.sleep(5)
   output$text <- renderText("Output is generated")
  }
  
  observeEvent(input$click, {
    call_fun(input, output)
  })
  
}

shinyApp(ui, server)

Sys.sleep(5) is to mimic a process that takes time.

Now I'm trying to implement the same with callr. This is what I have.

library(shiny)

ui <- fluidPage(
  actionButton("click", "click me!"),
  textOutput("text")
)

server <- function(input, output, session) {
  rv <- reactiveValues(callr = NULL)
  
  call_fun <- function(input, output) {
    Sys.sleep(5)
    output$text <- shiny::renderText("Output is generated")
  }
  
  observeEvent(input$click, {
    rv$callr <- callr::r_bg(function(input, output, call_fun) call_fun(input, output), 
                  args = list(input, output, call_fun))
  })
  
  observe({
    req(rv$callr)
    cat('\nIn Observe')
    if(rv$callr$is_alive()) {
      invalidateLater(millis = 1000, session = session)
      cat('\nProcessing')
    }
    else {
      cat("\nDone")
    }
  })
  
}

shinyApp(ui, server)

I do get the "Done" in console but I don't see the text output on screen.

Any idea how to solve this?