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/tsconfig.json

@@ -0,0 +1,18 @@
+{
+  "compilerOptions": {
+    "target": "ES2022",
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "strict": true,
+    "esModuleInterop": true,
+    "skipLibCheck": true,
+    "forceConsistentCasingInFileNames": true,
+    "outDir": "dist",
+    "rootDir": "src",
+    "declaration": false,
+    "sourceMap": true,
+    "lib": ["ES2022", "DOM"],
+    "types": ["chrome"]
+  },
+  "include": ["src/**/*.ts"]
+}