feat: add index route with auth guard and redirect logic

studio/frontend/src/app/router.tsx

@@ -2,6 +2,7 @@ import { createRouter } from "@tanstack/react-router";
 import { Route as rootRoute } from "./routes/__root";
 import { Route as chatRoute } from "./routes/chat";
 import { Route as gridTestRoute } from "./routes/grid-test";
+import { Route as indexRoute } from "./routes/index";
 import { Route as loginRoute } from "./routes/login";
 import { Route as onboardingRoute } from "./routes/onboarding";
 import { Route as exportRoute } from "./routes/export";
@@ -9,6 +10,7 @@ import { Route as signupRoute } from "./routes/signup";
 import { Route as studioRoute } from "./routes/studio";
 
 const routeTree = rootRoute.addChildren([
+  indexRoute,
   onboardingRoute,
   loginRoute,
   signupRoute,

studio/frontend/src/app/routes/index.tsx

@@ -0,0 +1,14 @@
+import { createRoute, redirect } from "@tanstack/react-router";
+import { getPostAuthRoute } from "@/features/auth";
+import { requireAuth } from "../auth-guards";
+import { Route as rootRoute } from "./__root";
+
+export const Route = createRoute({
+  getParentRoute: () => rootRoute,
+  path: "/",
+  beforeLoad: async () => {
+    await requireAuth();
+    throw redirect({ to: getPostAuthRoute() });
+  },
+  component: () => null,
+});