feat: Add Remote TeleBot Discovery & Configuration

- Add discovery API endpoints to TeleBot (probe, initialize, configure, status)
- Add LivenessService for LittleShop connectivity monitoring with 5min shutdown
- Add BotDiscoveryService to LittleShop for remote bot management
- Add Admin UI: DiscoverRemote wizard, RepushConfig page, status badges
- Add remote discovery fields to Bot model (RemoteAddress, RemotePort, etc.)
- Add CheckRemoteStatus and RepushConfig controller actions
- Update Index/Details views to show remote bot indicators
- Shared secret authentication for discovery, BotKey for post-init

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

LittleShop/Areas/Admin/Views/Bots/Index.cshtml

@@ -7,6 +7,9 @@
 <h1>Bot Management</h1>
 
 <p>
+    <a href="/Admin/Bots/DiscoverRemote" class="btn btn-success">
+        <i class="fas fa-satellite-dish"></i> Discover Remote Bot
+    </a>
     <a href="/Admin/Bots/Wizard" class="btn btn-primary">
         <i class="fas fa-magic"></i> Create Telegram Bot (Wizard)
     </a>
@@ -136,6 +139,12 @@
                         {
                             <span class="badge bg-secondary ms-2">@bot.PersonalityName</span>
                         }
+                        @if (bot.IsRemote)
+                        {
+                            <span class="badge bg-info ms-1" title="Remote bot at @bot.RemoteAddress:@bot.RemotePort">
+                                <i class="fas fa-satellite-dish"></i> Remote
+                            </span>
+                        }
                         @if (!string.IsNullOrEmpty(bot.Description))
                         {
                             <br />
@@ -181,6 +190,37 @@
                                 <span class="badge bg-dark">@bot.Status</span>
                                 break;
                         }
+                        @if (bot.IsRemote)
+                        {
+                            <br />
+                            @switch (bot.DiscoveryStatus)
+                            {
+                                case "Configured":
+                                    <span class="badge bg-success small mt-1" title="Remote bot is fully configured">
+                                        <i class="fas fa-check"></i> Configured
+                                    </span>
+                                    break;
+                                case "Initialized":
+                                    <span class="badge bg-info small mt-1" title="Remote bot initialized, awaiting config">
+                                        <i class="fas fa-clock"></i> Initialized
+                                    </span>
+                                    break;
+                                case "Discovered":
+                                    <span class="badge bg-warning small mt-1" title="Remote bot discovered, needs setup">
+                                        <i class="fas fa-exclamation"></i> Needs Setup
+                                    </span>
+                                    break;
+                                case "Offline":
+                                case "Error":
+                                    <span class="badge bg-danger small mt-1" title="Remote bot is offline or errored">
+                                        <i class="fas fa-times"></i> @bot.DiscoveryStatus
+                                    </span>
+                                    break;
+                                default:
+                                    <span class="badge bg-secondary small mt-1">@bot.DiscoveryStatus</span>
+                                    break;
+                            }
+                        }
                     </td>
                     <td>
                         <span class="badge bg-primary">@bot.ActiveSessions</span>