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, 2 deletions

diff --git a/src/client/components/SyncButton.tsx b/src/client/components/SyncButton.tsx
index 1c214ad..805cb45 100644
--- a/src/client/components/SyncButton.tsx
+++ b/src/client/components/SyncButton.tsx
@@ -1,9 +1,12 @@
 import { faArrowsRotate, faSpinner } from "@fortawesome/free-solid-svg-icons";
 import { FontAwesomeIcon } from "@fortawesome/react-fontawesome";
-import { useSync } from "../stores";
+import { useAtomValue, useSetAtom } from "jotai";
+import { isOnlineAtom, isSyncingAtom, syncActionAtom } from "../atoms";
 
 export function SyncButton() {
-	const { isOnline, isSyncing, sync } = useSync();
+	const isOnline = useAtomValue(isOnlineAtom);
+	const isSyncing = useAtomValue(isSyncingAtom);
+	const sync = useSetAtom(syncActionAtom);
 
 	const handleSync = async () => {
 		await sync();