feat: implement authentication state management and routing logic

- Added a new auth store using Zustand to manage authentication state, including `authChecked` and `isAuthenticated`.
- Updated `LoginView` to set authentication state upon successful login and navigate based on setup completion.
- Enhanced `RootLayoutContent` to enforce routing rules based on authentication status, redirecting users to login or setup as necessary.
- Improved error handling and loading states during authentication checks.

apps/ui/src/store/auth-store.ts

@@ -0,0 +1,29 @@
+import { create } from 'zustand';
+
+interface AuthState {
+  /** Whether we've attempted to determine auth status for this page load */
+  authChecked: boolean;
+  /** Whether the user is currently authenticated (web mode: valid session cookie) */
+  isAuthenticated: boolean;
+}
+
+interface AuthActions {
+  setAuthState: (state: Partial<AuthState>) => void;
+  resetAuth: () => void;
+}
+
+const initialState: AuthState = {
+  authChecked: false,
+  isAuthenticated: false,
+};
+
+/**
+ * Web authentication state.
+ *
+ * Intentionally NOT persisted: source of truth is the server session cookie.
+ */
+export const useAuthStore = create<AuthState & AuthActions>((set) => ({
+  ...initialState,
+  setAuthState: (state) => set(state),
+  resetAuth: () => set(initialState),
+}));