Remove staging from spacetimeauth docs and update react integration

docs/docs/spacetimeauth/react-integration.md

@@ -27,9 +27,10 @@ SpacetimeAuth dashboard.
 
 ```tsx
 const oidcConfig = {
-  authority: 'https://spacetimeauth.staging.spacetimedb.com/oidc',
+  authority: 'https://auth.spacetimedb.com/oidc',
   client_id: 'YOUR_CLIENT_ID',
-  redirect_uri: `${window.location.origin}/callback`,
+  redirect_uri: `${window.location.origin}/callback`, // Where the user is redirected after login
+  post_logout_redirect_uri: window.location.origin, // Where the user is redirected after logout
   scope: 'openid profile email',
   response_type: 'code',
   automaticSilentRenew: true,
@@ -123,5 +124,41 @@ root.render(
 
 ```
 
+### 4. Implement Authentication Logic in Your App
+
+In your main component (e.g., `App.tsx`), use the `useAutoSignin` hook to automatically
+sign in users if they are not authenticated.
+
+```tsx
+import React from 'react';
+import { useAuth, useAutoSignin } from 'react-oidc-context';
+import './App.css';
+function App() {
+  const auth = useAuth();
+  useAutoSignin();
+
+  if (auth.isLoading) {
+    return <div>Loading...</div>;
+  }
+
+  if (auth.error) {
+    return <div>Error: {auth.error.message}</div>;
+  }
+
+  if (!auth.isAuthenticated) {
+    return <div>Redirecting to login...</div>;
+  }
+
+  return (
+    <div className="App">
+      <header className="App-header">
+          Welcome, {auth.user?.profile.name} (id: {auth.user?.profile.sub})!
+        <button onClick={() => auth.signoutRedirect()}>Sign Out</button>
+      </header>
+    </div>
+  );
+}
+
 You're now set up to use SpacetimeAuth in your React application. When users
 access your app, they will be redirected to the SpacetimeAuth login page for authentication.
+```