feat(client): add sync status indicator component

Add SyncStatusIndicator component to display current sync state in the
UI header. The component shows online/offline status, syncing progress,
pending changes count, and sync errors.

- Create SyncProvider context to wrap SyncManager for React components
- Add SyncStatusIndicator component with visual status indicators
- Integrate indicator into HomePage header
- Add comprehensive tests for SyncStatusIndicator and SyncProvider
- Update existing tests to include SyncProvider wrapper

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

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

1 files changed, 33 insertions, 36 deletions

diff --git a/src/client/sync/index.ts b/src/client/sync/index.ts
index a602753..c3ddab4 100644
--- a/src/client/sync/index.ts
+++ b/src/client/sync/index.ts
@@ -1,50 +1,47 @@
 export {
-	SyncQueue,
-	SyncStatus,
-	syncQueue,
-	type PendingChanges,
-	type SyncQueueListener,
-	type SyncQueueState,
-	type SyncStatusType,
-} from "./queue";
-
+	type ConflictResolutionItem,
+	type ConflictResolutionResult,
+	ConflictResolver,
+	type ConflictResolverOptions,
+	conflictResolver,
+	createConflictResolver,
+} from "./conflict";
 export {
-	createPushService,
-	pendingChangesToPushData,
-	PushService,
-	type PushServiceOptions,
-	type SyncCardData,
-	type SyncDeckData,
-	type SyncPushData,
-	type SyncPushResult,
-	type SyncReviewLogData,
-} from "./push";
+	createSyncManager,
+	SyncManager,
+	type SyncManagerEvent,
+	type SyncManagerListener,
+	type SyncManagerOptions,
+	type SyncResult,
+} from "./manager";
 
 export {
 	createPullService,
-	pullResultToLocalData,
 	PullService,
 	type PullServiceOptions,
+	pullResultToLocalData,
 	type ServerCard,
 	type ServerDeck,
 	type ServerReviewLog,
 	type SyncPullResult,
 } from "./pull";
-
 export {
-	ConflictResolver,
-	conflictResolver,
-	createConflictResolver,
-	type ConflictResolutionItem,
-	type ConflictResolutionResult,
-	type ConflictResolverOptions,
-} from "./conflict";
-
+	createPushService,
+	PushService,
+	type PushServiceOptions,
+	pendingChangesToPushData,
+	type SyncCardData,
+	type SyncDeckData,
+	type SyncPushData,
+	type SyncPushResult,
+	type SyncReviewLogData,
+} from "./push";
 export {
-	createSyncManager,
-	SyncManager,
-	type SyncManagerEvent,
-	type SyncManagerListener,
-	type SyncManagerOptions,
-	type SyncResult,
-} from "./manager";
+	type PendingChanges,
+	SyncQueue,
+	type SyncQueueListener,
+	type SyncQueueState,
+	SyncStatus,
+	type SyncStatusType,
+	syncQueue,
+} from "./queue";