docs: Update documentation for controller PR #2315 (#198)

Updates documentation to reflect changes made in:
    feat: add headless mode support to controller SDK

    Related controller PR: cartridge-gg/controller#2315

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>

Author: tarrencev

src/pages/controller/examples/react.md

@@ -258,7 +258,104 @@ export function MultiAuthConnectWallet() {
 }
 ```
 
-### 4. Performing Transactions
+### 4. Headless Authentication
+
+For programmatic authentication without opening any UI, you can use headless mode in your React components:
+
+```tsx
+import { useCallback, useState } from 'react'
+import { useConnect } from '@starknet-react/core'
+import { ControllerConnector } from '@cartridge/connector'
+
+export function HeadlessLogin() {
+  const { connectAsync, connectors } = useConnect()
+  const [username, setUsername] = useState('')
+  const [loading, setLoading] = useState(false)
+  const controller = connectors[0] as ControllerConnector
+
+  const handleHeadlessLogin = useCallback(async (signer: string) => {
+    if (!username) {
+      alert('Please enter a username')
+      return
+    }
+
+    setLoading(true)
+    try {
+      // Ensure we start fresh
+      if (controller.account) {
+        await controller.disconnect()
+      }
+
+      // Headless authentication
+      const account = await controller.connect({
+        username,
+        signer,
+      })
+
+      if (!account) {
+        throw new Error('Failed to authenticate')
+      }
+
+      // Sync with starknet-react state
+      await connectAsync({ connector: controller })
+      
+      alert(`Successfully authenticated as ${username}!`)
+    } catch (error) {
+      console.error('Headless authentication failed:', error)
+      alert('Authentication failed: ' + (error as Error).message)
+    } finally {
+      setLoading(false)
+    }
+  }, [username, controller, connectAsync])
+
+  return (
+    <div className="space-y-4">
+      <div>
+        <label htmlFor="username">Username:</label>
+        <input
+          id="username"
+          type="text"
+          value={username}
+          onChange={(e) => setUsername(e.target.value)}
+          placeholder="Enter your username"
+          disabled={loading}
+        />
+      </div>
+      
+      <div className="grid gap-2">
+        <button 
+          onClick={() => handleHeadlessLogin('webauthn')}
+          disabled={loading || !username}
+        >
+          Login with Passkey
+        </button>
+        
+        <button 
+          onClick={() => handleHeadlessLogin('metamask')}
+          disabled={loading || !username}
+        >
+          Login with MetaMask
+        </button>
+        
+        <button 
+          onClick={() => handleHeadlessLogin('google')}
+          disabled={loading || !username}
+        >
+          Login with Google
+        </button>
+      </div>
+      
+      {loading && <p>Authenticating...</p>}
+    </div>
+  )
+}
+```
+
+:::warning
+Headless mode requires that the user already has the specified signer (passkey, OAuth account, EVM wallet) associated with their Cartridge username. For new user registration, use the regular `connect()` flow which opens the UI.
+:::
+
+### 5. Performing Transactions
 
 Execute transactions using the `account` object from `useAccount` hook:
 

src/pages/controller/getting-started.mdx

@@ -35,6 +35,41 @@ const account = await controller.connect();
 const phantomAccount = await controller.connect(["phantom-evm"]);
 ```
 
+### Headless Authentication
+
+For programmatic authentication without opening any UI, you can use headless mode by providing a `username` and `signer`:
+
+```ts
+import Controller from "@cartridge/controller";
+
+const controller = new Controller({});
+
+// Headless authentication with WebAuthn/Passkey
+const account = await controller.connect({
+  username: "alice",
+  signer: "webauthn",
+});
+
+// Headless authentication with password
+const account = await controller.connect({
+  username: "alice",
+  signer: "password",
+  password: "your-secure-password",
+});
+
+// Headless authentication with OAuth providers
+await controller.connect({ username: "alice", signer: "google" });
+await controller.connect({ username: "alice", signer: "discord" });
+
+// Headless authentication with EVM wallets
+await controller.connect({ username: "alice", signer: "metamask" });
+await controller.connect({ username: "alice", signer: "phantom-evm" });
+```
+
+:::info
+Headless mode performs authentication in a hidden iframe without displaying any UI. However, if session policies need approval or verification, the UI will open automatically to request user consent.
+:::
+
 When `connect()` is called, users will see an improved controller creation interface with username autocomplete functionality. As users type their username, they'll see matching existing accounts with user profiles, making it easier to connect to existing controllers or choose unique usernames for new accounts.
 
 For session-based applications, users will see permissions organized into clear sections: an expandable "Authorize [game]" card containing contract methods, followed by dedicated spending limit cards for token approvals, making it easy to understand what they're authorizing.