How to update dropdown list based on the output of action button in shiny?

Your code could use a lot of work and I suggest you take a look at reactiveValues and eventReactive and not using functions in your server file for example - I actually started rewriting your entire app but then decided to focus on the question at hand.

Here is a start:

library(shinydashboard)
library(leaflet)
library(ggplot2)
library(DT)
library(openxlsx)

# -----------------------------------------------------------------------------
# Dashboard UI
# -----------------------------------------------------------------------------

dataset <- c("P1-Long-Term-Unemployment-Statistics","P1-OfficeSupplies","P1-SuperStoreUS-2015")
ui <- dashboardPage(
    dashboardHeader(
        title = "Validation Tool"
    ),
    dashboardSidebar(
        sidebarMenu(
            menuItem("Upload File", tabName = "file", icon = icon("database")),
            menuItem("View Tables", tabName = "view", icon = icon("database")),
            menuItem("Append Data", tabName = "append", icon = icon("database")),
            menuItem("Update Table", tabName = "update", icon = icon("crosshairs")),
            menuItem("Construct Table", tabName = "construct", icon = icon("fire"))
        ),

        div(style = "padding-left: 15px;padding-right: 5px; padding-top: 40px;",
            p(class = "small", "Note : This validation tools automates the mainstream process involved in creating a Master data for detailed analysis ")
        )
    ),
    dashboardBody(
        tabItems(
            # Current location ------------------------------------------------------
            tabItem(tabName = "view",
                    mainPanel(
                        titlePanel(h2("Explore Datasets")),fluidRow(
                            column(6,
                                   uiOutput("tables")
                            ),
                            column(6,
                                   uiOutput("sheets")
                            )

                        ),
                        tabsetPanel(type="tab", 
                                    tabPanel("Data",br(),div(DT::dataTableOutput("table"),style = "font-size: 100%;width: 150%")                           
                                    ),
                                    tabPanel("Summary"),
                                    tabPanel("Plot")
                        )
                    )
            ),
            ##################### Tab Item 2 Begins ###########################

            tabItem(tabName = "file",
                    mainPanel(
                        titlePanel(h2("Upload your XLSX file here ")), fluidRow(
                            column(6,
                                   fileInput('file1', 'Choose a XLSX file to upload',
                                             accept = c('.xlsx'))),
                            column(6,actionButton("save","Save to Database")),
                            div(DT::dataTableOutput("contents"),style = "font-size: 100%;width: 150%")
                        )

                    )
            )
            #####################End of Tab Item 2#############################
        )
    )
)

# -----------------------------------------------------------------------------
# Dashboard server code
# -----------------------------------------------------------------------------
options(shiny.maxRequestSize = 30*1024^2)

validate_file <- function(input) {
    if (length(input) > 0 & !is.null(input) & input!= "application/vnd.openxmlformats-officedocument.spreadsheetml.sheet") {
        "Please upload a XLSX file"
    } else {
        NULL
    }
}

server <- function(input, output,session) {

    my_file <- function(){  
        my_file <- paste0("D:/Dataset/",input$table,".xlsx")
    }

    sheetNames <- function(){
        sheetNames <- getSheetNames(my_file())
    }


    output$sheets <- renderUI({
        selectInput("sheet","Sheet:",choices = sheetNames())
    })

    tablelist<-c()

    output$tables <- renderUI({
        selectInput("table","Table:",choices = files())
    })


    output$table <- renderDT(read.xlsx(my_file(),sheet=as.character(input$sheet)),class="display nowrap compact",
                             filter = "top",options = list(
                                 scrollX = T,
                                 scrollCollapse=TRUE, pageLength=20,scrollY="260px",lengthMenu=c(20,40,60,80,100),
                                 search = list(regex = FALSE, caseInsensitive = FALSE)))



    # output$contents <- renderTable({
    #   # input$file1 will be NULL initially. After the user selects
    #   # and uploads a file, it will be a data frame with 'name',
    #   # 'size', 'type', and 'datapath' columns. The 'datapath'
    #   # column will contain the local filenames where the data can
    #   # be found.
    # 
    #   inFile <- input$file1
    #   if (is.null(inFile))
    #     return(NULL)
    #   read.xlsx(inFile$name, sheet=1)
    # })


    ############################## Validate Scenario ########################


    v <- reactive({
        type <- input$file1
        validate(validate_file(type$type))
    })

    ############################# Scenario Ends ############################


    output$contents <- renderDT({
        # input$file1 will be NULL initially. After the user selects
        # and uploads a file, it will be a data frame with 'name',
        # 'size', 'type', and 'datapath' columns. The 'datapath'
        # column will contain the local filenames where the data can
        # be found.
        inFile <- req(input$file1)
        v()
        if (is.null(inFile))
            return(NULL)
        read.xlsx(inFile$datapath, sheet=1)
    },class="display nowrap compact",
    options = list(
        scrollX = T,
        pageLength=20,scrollY="340px",lengthMenu=c(20,40,60,80,100)
    ))


    ############################# ACtion Button Save ######################################


    files <- eventReactive(input$save,{

            filenm <- input$file1
            filenm$name

            tablelist <- c(tablelist,as.character(filenm$name))
            filePath <- c(filePath,as.character(filenm$dataPath))

        return (tablelist)
    })




    ############################# End of Action button ####################################

}

shinyApp(ui, server)

I moved inFile <- req(input$file1) before v() and added the req() to remove the initial error message on loading the app but the main work was in this piece:

    files <- eventReactive(input$save,{

            filenm <- input$file1
            filenm$name

            tablelist <- c(tablelist,as.character(filenm$name))
            filePath <- c(filePath,as.character(filenm$dataPath))

        return (tablelist)
    })

and then changing files to files() here:

    output$tables <- renderUI({
        selectInput("table","Table:",choices = files())
    })

This should answer your current question but there are lots of other issues with your app so let me know when they come up.