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/src/css/tabs.css

@@ -309,6 +309,36 @@
     background: var(--bg-active);
 }
 
+/* -----------------------------------------------------------------------
+   Broadcast toggle button
+   ----------------------------------------------------------------------- */
+.tab-broadcast {
+    display: flex;
+    align-items: center;
+    justify-content: center;
+    width: var(--tab-bar-height);
+    height: var(--tab-bar-height);
+    color: var(--text-tertiary);
+    cursor: pointer;
+    flex-shrink: 0;
+    transition: background var(--transition-fast), color var(--transition-fast);
+    border: none;
+    background: none;
+    opacity: 0.5;
+}
+
+.tab-broadcast:hover {
+    background: var(--bg-hover);
+    color: var(--text-primary);
+    opacity: 0.8;
+}
+
+.tab-broadcast.is-active {
+    color: var(--error);
+    opacity: 1;
+    animation: pulse-dot 1.5s ease infinite;
+}
+
 /* -----------------------------------------------------------------------
    Tab overflow indicators (chevrons at edges)
    ----------------------------------------------------------------------- */