feat: Chrome extension Side Panel + Conductor API proposal

Chrome extension (Manifest V3, sideload):
- Side Panel with live activity feed, @ref overlays, dark terminal aesthetic
- Background worker: health polling, SSE relay, ref fetching
- Popup: port config, connection status, side panel launcher
- Content script: floating ref panel with @ref badges

Conductor API proposal (docs/designs/CONDUCTOR_SESSION_API.md):
- SSE endpoint for full Claude Code session mirroring in Side Panel
- Discovery via HTTP endpoint (not filesystem — extensions can't read files)

TODOS.md: add $B watch, multi-agent tabs, cross-platform CDP, Web Store publishing.
Mark CDP mode as shipped.

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

extension/popup.js

@@ -0,0 +1,60 @@
+const portInput = document.getElementById('port');
+const dot = document.getElementById('dot');
+const statusText = document.getElementById('status-text');
+const details = document.getElementById('details');
+const sidePanelBtn = document.getElementById('side-panel-btn');
+
+// Load saved port
+chrome.runtime.sendMessage({ type: 'getPort' }, (resp) => {
+  if (resp && resp.port) {
+    portInput.value = resp.port;
+    updateStatus(resp.connected);
+  }
+});
+
+// Save port on change
+let saveTimeout;
+portInput.addEventListener('input', () => {
+  clearTimeout(saveTimeout);
+  saveTimeout = setTimeout(() => {
+    const port = parseInt(portInput.value, 10);
+    if (port > 0 && port < 65536) {
+      chrome.runtime.sendMessage({ type: 'setPort', port });
+    }
+  }, 500);
+});
+
+// Listen for health updates
+chrome.runtime.onMessage.addListener((msg) => {
+  if (msg.type === 'health') {
+    updateStatus(!!msg.data, msg.data);
+  }
+});
+
+function updateStatus(connected, data) {
+  dot.className = `dot ${connected ? 'connected' : ''}`;
+  statusText.className = `status-text ${connected ? 'connected' : ''}`;
+  statusText.textContent = connected ? 'Connected' : 'Disconnected';
+
+  if (connected && data) {
+    const parts = [];
+    if (data.tabs) parts.push(`${data.tabs} tabs`);
+    if (data.mode) parts.push(`Mode: ${data.mode}`);
+    details.textContent = parts.join(' \u00b7 ');
+  } else {
+    details.textContent = '';
+  }
+}
+
+// Open side panel
+sidePanelBtn.addEventListener('click', async () => {
+  try {
+    const [tab] = await chrome.tabs.query({ active: true, currentWindow: true });
+    if (tab) {
+      await chrome.sidePanel.open({ tabId: tab.id });
+      window.close();
+    }
+  } catch (err) {
+    details.textContent = `Side panel error: ${err.message}`;
+  }
+});