refactor(client): migrate state management from React Context to Jotai

Replace AuthProvider and SyncProvider with Jotai atoms for more granular
state management and better performance. This migration:

- Creates atoms for auth, sync, decks, cards, noteTypes, and study state
- Uses atomFamily for parameterized state (e.g., cards by deckId)
- Introduces StoreInitializer component for subscription initialization
- Updates all components and pages to use useAtomValue/useSetAtom
- Updates all tests to use Jotai Provider with createStore pattern

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

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

1 files changed, 12 insertions, 0 deletions

diff --git a/src/client/components/StoreInitializer.tsx b/src/client/components/StoreInitializer.tsx
new file mode 100644
index 0000000..a6ddefc
--- /dev/null
+++ b/src/client/components/StoreInitializer.tsx
@@ -0,0 +1,12 @@
+import type { ReactNode } from "react";
+import { useAuthInit, useSyncInit } from "../atoms";
+
+interface StoreInitializerProps {
+	children: ReactNode;
+}
+
+export function StoreInitializer({ children }: StoreInitializerProps) {
+	useAuthInit();
+	useSyncInit();
+	return <>{children}</>;
+}