fix: disable idle timeout in headed mode — browser lives until closed

The 30-minute idle timeout only applies to headless mode now. In headed
mode the user is looking at the Chrome window, so auto-shutdown is wrong.
The browser stays alive until explicit disconnect or window close.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

browse/src/server.ts

@@ -675,6 +675,9 @@ function resetIdleTimer() {
 }
 
 const idleCheckInterval = setInterval(() => {
+  // Headed mode: the user is looking at the browser. Never auto-die.
+  // Only shut down when the user explicitly disconnects or closes the window.
+  if (browserManager.getConnectionMode() === 'headed') return;
   if (Date.now() - lastActivity > IDLE_TIMEOUT_MS) {
     console.log(`[browse] Idle for ${IDLE_TIMEOUT_MS / 1000}s, shutting down`);
     shutdown();