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, 5 insertions, 3 deletions

diff --git a/src/client/components/ProtectedRoute.tsx b/src/client/components/ProtectedRoute.tsx
index 76b663c..a0eb2ee 100644
--- a/src/client/components/ProtectedRoute.tsx
+++ b/src/client/components/ProtectedRoute.tsx
@@ -1,16 +1,18 @@
+import { useAtomValue } from "jotai";
 import type { ReactNode } from "react";
 import { Redirect } from "wouter";
-import { useAuth } from "../stores";
+import { authLoadingAtom, isAuthenticatedAtom } from "../atoms";
 
 export interface ProtectedRouteProps {
 	children: ReactNode;
 }
 
 export function ProtectedRoute({ children }: ProtectedRouteProps) {
-	const { isAuthenticated, isLoading } = useAuth();
+	const isAuthenticated = useAtomValue(isAuthenticatedAtom);
+	const isLoading = useAtomValue(authLoadingAtom);
 
 	if (isLoading) {
-		return <div>Loading...</div>;
+		return <output>Loading...</output>;
 	}
 
 	if (!isAuthenticated) {