feat(sync): auto-refresh on Jellyfin LibraryChanged events

Handle the server's LibraryChanged WebSocket message to invalidate
library-dependent React Query caches when items are added/updated/
removed, so newly added episodes/movies appear without a manual
refresh. Debounced to coalesce a scan's burst of events.

Add useRefreshLibraryOnFocus as a fallback that re-checks on screen
focus (throttled, online-only, skips first focus), wired into home
(mobile + TV) and the library pages.

hooks/useRefreshLibraryOnFocus.ts

@@ -0,0 +1,50 @@
+import { useFocusEffect } from "expo-router";
+import { useCallback, useRef } from "react";
+import { useNetworkAwareQueryClient } from "@/hooks/useNetworkAwareQueryClient";
+
+// Query keys that depend on the set of library items. Kept in sync with the
+// LibraryChanged handler in WebSocketProvider.
+const LIBRARY_QUERY_KEYS = [
+  ["home"],
+  ["library-items"],
+  ["nextUp-all"],
+  ["nextUp"],
+  ["resumeItems"],
+];
+
+/**
+ * Fallback refresh for newly added/removed content.
+ *
+ * The primary path is the server's `LibraryChanged` WebSocket event (handled in
+ * WebSocketProvider). This hook is a safety net for cases where the socket was
+ * down or the change happened while the screen was unfocused: when the screen
+ * regains focus, it invalidates the library-dependent queries so React Query
+ * refetches the latest content.
+ *
+ * Skips the refresh on the very first focus (initial mount already fetches) and
+ * throttles to avoid refetch storms when quickly switching tabs.
+ */
+export function useRefreshLibraryOnFocus(throttleMs = 30_000) {
+  const queryClient = useNetworkAwareQueryClient();
+  const hasFocusedOnce = useRef(false);
+  const lastRefreshRef = useRef(0);
+
+  useFocusEffect(
+    useCallback(() => {
+      if (!hasFocusedOnce.current) {
+        hasFocusedOnce.current = true;
+        return;
+      }
+
+      const now = Date.now();
+      if (now - lastRefreshRef.current < throttleMs) {
+        return;
+      }
+      lastRefreshRef.current = now;
+
+      for (const queryKey of LIBRARY_QUERY_KEYS) {
+        queryClient.invalidateQueries({ queryKey });
+      }
+    }, [queryClient, throttleMs]),
+  );
+}