fix: sidebar chat resets idle timer + shutdown kills sidebar-agent

Two fixes for the "browser died while chatting" problem:

1. /sidebar-command now calls resetIdleTimer(). Previously only CLI
   commands reset it, so the server would shut down after 30 min even
   while the user was actively chatting in the sidebar.

2. shutdown() now pkills the sidebar-agent daemon. Previously the agent
   survived server shutdown, kept polling a dead server, and spawned
   confused claude processes that auto-started headless browsers.

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

browse/src/server.ts

@@ -915,6 +915,15 @@ async function shutdown() {
   isShuttingDown = true;
 
   console.log('[browse] Shutting down...');
+  // Kill the sidebar-agent daemon process (spawned by cli.ts, detached).
+  // Without this, the agent keeps polling a dead server and spawns confused
+  // claude processes that auto-start headless browsers.
+  try {
+    const { spawnSync } = require('child_process');
+    spawnSync('pkill', ['-f', 'sidebar-agent\\.ts'], { stdio: 'ignore', timeout: 3000 });
+  } catch (err: any) {
+    console.warn('[browse] Failed to kill sidebar-agent:', err.message);
+  }
   // Clean up CDP inspector sessions
   try { detachSession(); } catch (err: any) {
     console.warn('[browse] Failed to detach CDP session:', err.message);
@@ -1265,6 +1274,7 @@ async function start() {
         if (!validateAuth(req)) {
           return new Response(JSON.stringify({ error: 'Unauthorized' }), { status: 401, headers: { 'Content-Type': 'application/json' } });
         }
+        resetIdleTimer(); // Sidebar chat is real user activity
         const body = await req.json();
         const msg = body.message?.trim();
         if (!msg) {