Dynamic number of actionButtons tied to unique observeEvent

Your really close, just wrap the observeEvent part in local.

library(shiny)

ui <- basicPage(
  fluidRow(
    actionButton(inputId = "add_button",
                 label = "Add Button")
  ),
  uiOutput("more_buttons")
)

server <- function(input, output){

  rvs      <- reactiveValues(buttons = list(actionButton(inputId = "button1",
                                                    label = 1)))

  observeEvent(eventExpr = input$add_button,
               handlerExpr = {
                 len      <- length(rvs$buttons) + 1
                 rvs$buttons[[len]] <- actionButton(inputId = paste0("button",len),
                                                    label = len)
               })

  output$more_buttons <- renderUI({
    do.call(fluidRow, rvs$buttons)
  })

  observeEvent(rvs$buttons,{
    for(ii in 1:length(rvs$buttons)){
      local({
        i <- ii
        observeEvent(eventExpr = input[[paste0("button",i)]],
                     handlerExpr = {print(sprintf("You clicked btn number %d",i))})
      })
    }
  })

}

shinyApp(ui, server)