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, 8 insertions, 0 deletions

diff --git a/src/client/stores/index.ts b/src/client/stores/index.ts
index 7117bd6..c7f6241 100644
--- a/src/client/stores/index.ts
+++ b/src/client/stores/index.ts
@@ -5,3 +5,11 @@ export type {
 	AuthState,
 } from "./auth";
 export { ApiClientError, AuthProvider, useAuth } from "./auth";
+
+export type {
+	SyncActions,
+	SyncContextValue,
+	SyncProviderProps,
+	SyncState,
+} from "./sync";
+export { SyncProvider, useSync } from "./sync";