How to wait for input widget updates until rendering output in Shiny?

Question

See the following nonsense minimal-working example that resembles a problem:

library(shiny)
ui = shiny::fluidPage(

    shiny::sidebarLayout(
        shiny::sidebarPanel(
            shiny::radioButtons("type", "Type", choices = c("5", "15", "21")),
            shiny::sliderInput("x", "x", min = 1, max = 10, value = 7),
            shiny::checkboxInput("auto","Set y to 8 when type is 15, and 9 when type is 21", value = TRUE),
            shiny::sliderInput("y", "y", min = 1, max = 10, value = 7)
        ),

        shiny::mainPanel(
            shiny::plotOutput("show")
        )
    )
)
server = function(input, output, session) {
    plotData = shiny::reactive({
        list(x = input$x, y = input$y, type = input$type)
    })

    output$show = renderPlot({
        shiny::req(plotData())
        d = plotData()
        print("refresh")
        plot(d$x,d$y, pch = as.integer(d$type))
    })


    observe({
        n = input$n
        a = input$auto
        type = input$type

        if (type == "a") return(NULL)
        if (a) shiny::updateSliderInput(session, "y", value = switch(type, "15" = 8, "21" = 9))
    })
}
shiny::shinyApp(ui = ui, server = server)

The problem is that the plot is rendered twice when the user selects either type 15 or 21. That is caused by the fact that when plotData changes, updateSliderInput is executed before renderPlot. (I have seen this behavior with the reactlog package.) However, I don't know how to solve this. I've tried a bunch of functions, such as isolate, req, but without success.