feat: add AppState-aware WebSocket reconnect on mobile foreground

When the app returns from background, check if the WebSocket is still
open. If not, close the stale socket and reconnect with reset backoff.
Proactively close the WS when backgrounding to save battery and avoid
OS killing it mid-frame. Add "reconnecting" connection status with
amber pulsing badge so users see the app is re-establishing connection.

Fixes #33

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

artifacts/mobile/components/ConnectionBadge.tsx

@@ -11,6 +11,7 @@ const STATUS_CONFIG: Record<ConnectionStatus, { color: string; label: string }>
   connecting: { color: "#F59E0B", label: "Connecting" },
   connected: { color: "#10B981", label: "Live" },
   disconnected: { color: "#6B7280", label: "Offline" },
+  reconnecting: { color: "#F59E0B", label: "Reconnecting" },
   error: { color: "#EF4444", label: "Error" },
 };
 
@@ -18,7 +19,7 @@ export function ConnectionBadge({ status }: { status: ConnectionStatus }) {
   const pulseAnim = useRef(new Animated.Value(1)).current;
 
   useEffect(() => {
-    if (status === "connecting") {
+    if (status === "connecting" || status === "reconnecting") {
       const pulse = Animated.loop(
         Animated.sequence([
           Animated.timing(pulseAnim, { toValue: 0.3, duration: 600, useNativeDriver: true }),