Fix isHydrated state for Zustand persist

- Add onRehydrateStorage callback to set isHydrated
- Initialize isLoading to true and set to false after hydration
- Remove manual isHydrated check in page.tsx

frontend/src/lib/auth.ts

@@ -15,6 +15,7 @@ interface AuthState {
   logout: () => void
   login: (username: string, password: string) => Promise<void>
   checkAuth: () => Promise<void>
+  setHydrated: () => void
 }
 
 export const useAuth = create<AuthState>()(
@@ -23,10 +24,12 @@ export const useAuth = create<AuthState>()(
       token: null,
       refreshToken: null,
       user: null,
-      isLoading: false,
+      isLoading: true,
       isHydrated: false,
       error: null,
 
+      setHydrated: () => set({ isHydrated: true }),
+
       setAuth: (token, refreshToken, user) => {
         set({ token, refreshToken, user, error: null })
       },
@@ -101,6 +104,7 @@ export const useAuth = create<AuthState>()(
       onRehydrateStorage: () => (state) => {
         if (state) {
           state.isHydrated = true
+          state.isLoading = false
         }
       },
     }