fix: Root und 404 leiten unangemeldete User direkt zu /login

Bisher gingen "/" und unbekannte URLs immer erst zu /dashboard, das
dann bei fehlendem Login zu /login weiterleitete - unnoetiger Umweg.
Beide pruefen jetzt selbst den Auth-Status (gleiches Muster wie
(app)/layout.tsx: waehrend isLoading nichts tun, danach je nach User
direkt zu /dashboard oder /login).

ApiCore-Frontend/src/app/page.spec.tsx

@@ -1,14 +1,37 @@
-import { describe, expect, it, vi } from "vitest";
-import { redirect } from "next/navigation";
+import { beforeEach, describe, expect, it, vi } from "vitest";
+import { render } from "@testing-library/react";
 import Page from "./page";
 
+const replaceMock = vi.fn();
 vi.mock("next/navigation", () => ({
-  redirect: vi.fn(),
+  useRouter: () => ({ replace: replaceMock }),
+}));
+
+let mockAuth: { user: { id: string } | null; isLoading: boolean };
+vi.mock("@/lib/auth/auth-context", () => ({
+  useAuth: () => mockAuth,
 }));
 
 describe("Home page", () => {
-  it("redirects to the dashboard", () => {
-    Page();
-    expect(redirect).toHaveBeenCalledWith("/dashboard");
+  beforeEach(() => {
+    replaceMock.mockReset();
+  });
+
+  it("does not redirect while the auth check is still loading", () => {
+    mockAuth = { user: null, isLoading: true };
+    render(<Page />);
+    expect(replaceMock).not.toHaveBeenCalled();
+  });
+
+  it("redirects to the dashboard when logged in", () => {
+    mockAuth = { user: { id: "user-1" }, isLoading: false };
+    render(<Page />);
+    expect(replaceMock).toHaveBeenCalledWith("/dashboard");
+  });
+
+  it("redirects to login when not logged in", () => {
+    mockAuth = { user: null, isLoading: false };
+    render(<Page />);
+    expect(replaceMock).toHaveBeenCalledWith("/login");
   });
 });