feat: implement M2 Chrome browser extension

Build the CookieBridge Chrome extension (Manifest V3) with:

- Background service worker: cookie monitoring via chrome.cookies.onChanged,
  WebSocket connection to relay server with auto-reconnect, HTTP polling
  fallback, device registration and pairing flow
- Browser-compatible crypto: libsodium-wrappers-sumo for XChaCha20-Poly1305
  encryption, Ed25519 signing, X25519 key exchange (mirrors server's
  sodium-native API)
- Popup UI: device registration, connection status indicator (gray/blue/
  green/red), cookie/device/sync stats, one-click current site sync,
  whitelist quick-add, device pairing with 6-digit code
- Options page: server URL config, connection mode (auto/WS/polling),
  poll interval slider, auto-sync toggle, domain whitelist/blacklist
  management, paired device list, key export/import, data clearing
- Sync engine: LWW conflict resolution with Lamport clocks (same as
  server), bidirectional cookie sync with all paired peers, echo
  suppression to prevent sync loops
- Badge management: icon color reflects state (gray=not logged in,
  blue=connected, green=syncing with count, red=error)
- Build system: esbuild bundling for Chrome 120+, TypeScript with
  strict mode, clean type checking

Co-Authored-By: Paperclip <noreply@paperclip.ing>

extension/manifest.json

@@ -0,0 +1,32 @@
+{
+  "manifest_version": 3,
+  "name": "CookieBridge",
+  "version": "0.1.0",
+  "description": "Cross-device cookie synchronization with end-to-end encryption",
+  "permissions": [
+    "cookies",
+    "storage",
+    "alarms",
+    "tabs",
+    "activeTab"
+  ],
+  "host_permissions": ["<all_urls>"],
+  "background": {
+    "service_worker": "dist/background/service-worker.js",
+    "type": "module"
+  },
+  "action": {
+    "default_popup": "src/popup/popup.html",
+    "default_icon": {
+      "16": "src/icons/icon-gray-16.png",
+      "48": "src/icons/icon-gray-48.png",
+      "128": "src/icons/icon-gray-128.png"
+    }
+  },
+  "options_page": "src/options/options.html",
+  "icons": {
+    "16": "src/icons/icon-blue-16.png",
+    "48": "src/icons/icon-blue-48.png",
+    "128": "src/icons/icon-blue-128.png"
+  }
+}