Switch session storage from sessionStorage to localStorage

sessionStorage is per-tab — new tabs had no session, so WebSocket
didn't connect and real-time lock/booking sync didn't work.
localStorage shares session across tabs in the same browser.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/contexts/AuthContext.tsx

@@ -13,7 +13,7 @@ const AuthContext = createContext<AuthContextValue | null>(null)
 
 export function AuthProvider({ children }: { children: React.ReactNode }) {
   const [session, setSession] = useState<AuthSession | null>(() => {
-    const stored = sessionStorage.getItem('hotelsync-session')
+    const stored = localStorage.getItem('hotelsync-session')
     return stored ? JSON.parse(stored) : null
   })
 
@@ -22,7 +22,7 @@ export function AuthProvider({ children }: { children: React.ReactNode }) {
       const { access_token, user } = await api.auth.login(email, password)
       const s: AuthSession = { user, token: access_token }
       setSession(s)
-      sessionStorage.setItem('hotelsync-session', JSON.stringify(s))
+      localStorage.setItem('hotelsync-session', JSON.stringify(s))
       return user
     } catch (err) {
       if (err instanceof ApiError && err.status === 401) return null
@@ -33,7 +33,7 @@ export function AuthProvider({ children }: { children: React.ReactNode }) {
   const logout = async () => {
     try { await api.auth.logout() } catch { /* ignore */ }
     setSession(null)
-    sessionStorage.removeItem('hotelsync-session')
+    localStorage.removeItem('hotelsync-session')
   }
 
   return (