Add broadcast input mode for multi-session typing

Broadcast mode sends keystrokes from the active terminal to all other
connected sessions simultaneously. Useful for applying the same
commands across multiple servers.

- Toggle via Ctrl+Shift+B keyboard shortcut or broadcast button in tab bar
- Visual indicator: broadcast button pulses red when active
- Only sends to sessions in 'connected' state
- Notification on toggle
- State stored in app state object

frontend/index.html

@@ -128,6 +128,17 @@
                 <!-- Tabs are injected dynamically by JS -->
             </div>
             <button class="tab-new" id="btn-new-tab" title="New Tab">+</button>
+            <button class="tab-broadcast" id="btn-broadcast" title="Toggle Broadcast Mode (Ctrl+Shift+B)">
+                <!-- Broadcast icon (loudspeaker) -->
+                <svg xmlns="http://www.w3.org/2000/svg" width="12" height="12" viewBox="0 0 24 24"
+                     fill="none" stroke="currentColor" stroke-width="2"
+                     stroke-linecap="round" stroke-linejoin="round">
+                    <path d="M19.69 14a6.9 6.9 0 0 0 .31-2 6.9 6.9 0 0 0-.31-2"></path>
+                    <path d="M22.82 16.18a10 10 0 0 0 0-8.36"></path>
+                    <path d="M1 12s3-7 9-7 9 7 9 7-3 7-9 7-9-7-9-7z"></path>
+                    <circle cx="12" cy="12" r="3"></circle>
+                </svg>
+            </button>
         </div>
 
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