feat: cookies button in sidebar footer opens cookie picker

One-click cookie import from the sidebar. Navigates the headed browser
to /cookie-picker where you can select which domains to import from
your real Chrome profile.

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

extension/sidepanel.html

@@ -156,6 +156,7 @@
       <button class="debug-toggle" id="debug-toggle" title="Toggle debug panels">debug</button>
       <button class="footer-btn" id="clear-chat" title="Clear chat">clear</button>
       <button class="footer-btn" id="reload-sidebar" title="Reload sidebar">reload</button>
+      <button class="footer-btn" id="copy-cookies" title="Import cookies from your browser">cookies</button>
     </div>
     <div class="footer-right">
       <span class="dot" id="footer-dot"></span>

extension/sidepanel.js

@@ -636,6 +636,21 @@ document.getElementById('reload-sidebar').addEventListener('click', () => {
   location.reload();
 });
 
+// ─── Copy Cookies ───────────────────────────────────────────────
+document.getElementById('copy-cookies').addEventListener('click', async () => {
+  if (!serverUrl) return;
+  // Navigate the browser to the cookie picker page hosted by the browse server
+  try {
+    await fetch(`${serverUrl}/command`, {
+      method: 'POST',
+      headers: authHeaders(),
+      body: JSON.stringify({ command: 'goto', args: [`${serverUrl}/cookie-picker`] }),
+    });
+  } catch (err) {
+    console.error('[gstack sidebar] Failed to open cookie picker:', err.message);
+  }
+});
+
 // ─── Debug Tabs ─────────────────────────────────────────────────
 
 const debugToggle = document.getElementById('debug-toggle');