hotfix(frontend): fix home redirect (3) (#11904)

### Changes 🏗️

Further improvements to LaunchDarkly initialisation and homepage
redirect...

### Checklist 📋

#### For code changes:
- [x] I have clearly listed my changes in the PR description
- [x] I have made a test plan
- [x] I have tested my changes according to the test plan:
- [x] Run the app locally with the flag disabled/enabled, and the
redirects work

---------

Co-authored-by: claude[bot] <41898282+claude[bot]@users.noreply.github.com>
Co-authored-by: Ubbe <0ubbe@users.noreply.github.com>

autogpt_platform/frontend/src/app/page.tsx

@@ -1,11 +1,15 @@
-import { redirect } from "next/navigation";
+"use client";
+
+import { LoadingSpinner } from "@/components/atoms/LoadingSpinner/LoadingSpinner";
+import { useRouter } from "next/navigation";
+import { useEffect } from "react";
 
-/**
- * Root page always redirects to /copilot.
- * The /copilot page handles the feature flag check and redirects to /library if needed.
- * This single-check approach avoids race conditions with LaunchDarkly initialization.
- * See: SECRT-1845
- */
 export default function Page() {
-  redirect("/copilot");
+  const router = useRouter();
+
+  useEffect(() => {
+    router.replace("/copilot");
+  }, [router]);
+
+  return <LoadingSpinner size="large" cover />;
 }

autogpt_platform/frontend/src/services/feature-flags/feature-flag-provider.tsx

@@ -1,5 +1,6 @@
 "use client";
 
+import { LoadingSpinner } from "@/components/atoms/LoadingSpinner/LoadingSpinner";
 import { useSupabase } from "@/lib/supabase/hooks/useSupabase";
 import * as Sentry from "@sentry/nextjs";
 import { LDProvider } from "launchdarkly-react-client-sdk";
@@ -15,7 +16,9 @@ export function LaunchDarklyProvider({ children }: { children: ReactNode }) {
   const clientId = environment.getLaunchDarklyClientId();
 
   const context = useMemo(() => {
-    if (isUserLoading || !user) {
+    if (isUserLoading) return;
+
+    if (!user) {
       return {
         kind: "user" as const,
         key: "anonymous",
@@ -38,6 +41,10 @@ export function LaunchDarklyProvider({ children }: { children: ReactNode }) {
     return <>{children}</>;
   }
 
+  if (isUserLoading) {
+    return <LoadingSpinner size="large" cover />;
+  }
+
   return (
     <LDProvider
       clientSideID={clientId ?? ""}