How do I check if the current server is the newest server?

You can use the MarketplaceService which you can use GetProductInfo to return data about the asset. One value returned is the "Updated" which is the "Timestamp of the most recent time the author of the asset modified it "

Example:-

local hasUpdate  = false

spawn(function()
    local curTime = game:GetService("MarketplaceService"):GetProductInfo(game.PlaceId).Updated
    while true do
        hasUpdate  = ( curTime ==  game:GetService("MarketplaceService"):GetProductInfo(game.PlaceId).Updated)
        wait(1000)
    end
end)

-- other code

I hope this helps.