How do I save numeric inputs in Shiny during a session so they can be updated/overwritten by the user - r

Question

I'm look to create some functionality in a shiny app. I would like the user to be able to -
Click on an action button that opens up a modal to enter numeric inputs (the first time, values will be 0.
The user enters numeric inputs and hits "Submit"
A new dataframe is generated with the user's inputs.
If the user clicks the action button to open the modal again, the values that they entered the first time will still show as the default values.
Here is code to generate the basic app with the action button and modal. How do i edit this code for my usecase. I feel like I need to somehow set the value in the numericInput to read from some table that continually gets overwritten, but i'm not sure how to do it.
library(shiny)
library(tidyverse)
# Define the Shiny app UI
ui <- fluidPage(
# action button
actionButton(inputId = "edit_value", label = "Edit Value"),
# table output
verbatimTextOutput("table")
)
# Define the Shiny app server
server <- function(input, output, session) {
# reactive dataframe. this could have an unknown number of rows
df <- reactive({
tibble(
id = c(1, 2, 3, 4, 5),
name = c("Item1", "Item2", "Item3", "Item4", "Item5"),
value = c(0, 0, 0, 0, 0)
)
})
# modal pop up
observeEvent(eventExpr = input$edit_value, handlerExpr = {
showModal(modalDialog(
title = "Edit Value",
lapply(df()$name, function(name) {
numericInput(
inputId = paste0(name, "_value"),
label = name,
min = 0,
value = 0
)
}),
footer = tagList(
actionButton(inputId = "submit_add_value", label = "Submit"),
modalButton("Close")
)
))
})
# capture numeric inputs in modal pop up
temp_data <- eventReactive(input$submit_add_value, {
df() %>%
select(id, name) %>%
mutate(id = as.factor(id)) %>%
distinct() %>%
mutate(new_value = map_dbl(name, function(sym) {
input[[paste0(sym, "_value")]]
}))
})
# print numeric inputs in modal pop up
output$table <- renderPrint({temp_data()})
}
# Run the Shiny app
shinyApp(ui, server)