App.R

library(shiny)

# MODULE UI
customInputUI <- function(id) {
  ns <- NS(id)
  tagList(
    tags$div(
      HTML("
            <select id='yes_no'>
                <option value='yes'>Yes</option>
                <option value='no'>No</option>
           </select>")),
    verbatimTextOutput(ns("debug")),
    radioButtons(ns("my_radio"), "Radio", choices = c("Yes", "No"))
  )
}

# MODULE SERVER 
customInput <- function(input, output, session) {

  output$debug <- renderPrint({ input$testing })
  
  # Probably don't even need this
  observe({
    session$sendCustomMessage(type = 'testmessage', message = input$testing)
  })
  
}

# ACTUAL UI
ui <- fixedPage(
  customInputUI("custom_input"),

  
  tags$script(
    "
    // this works in vanialla JS
    // but here I get a weird ( syntax error?! 
    // $('#yes_no').change(function(){
    //    $('input[name='custom_input-my_radio'][value=' + $(this).val()  + ']')
    //       .prop('checked', true);
    //     }).trigger('change');

    // get the selected value from JS
    // on page load it's NULL but that's fine for now
    $('select#yes_no').change(function() {
       var selectedDropdown = $(this).children('option:selected').val();
       Shiny.setInputValue('custom_input-testing', selectedDropdown)
      // Set input$my_radio using setInputValue?
      // Shiny.setInputValue('custom_input-my_radio', $(this).val())
      });

    Shiny.addCustomMessageHandler('testmessage', function(message) {
    // leverage this to change input$my_radio using JS?
    console.log(message)
    });
    "
  )
  
)

# ACTUAL SERVER
server <- function(input, output, session) {
  df <- callModule(customInput, "custom_input")
}

shinyApp(ui, server)