feat(browser-ext): move browser extension to browser-ext/ and update API client to tRPC

- Create browser-ext/ with full extension code (MV3 manifest, background
  service worker, content script, popup, options page)
- Add tRPC API client that communicates with unified monolith endpoints
- Implement cache, settings, and phishing detection utilities
- Create extension tRPC router in web app (getAuthStatus, linkDevice,
  reportPhishing)
- Configure Vite build with manifest V3 support
- Write unit tests for cache, phishing detector, and API client
- All 20 tests passing, TypeScript lint clean

browser-ext/tsconfig.json

@@ -0,0 +1,15 @@
+{
+  "compilerOptions": {
+    "target": "ESNext",
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "allowSyntheticDefaultImports": true,
+    "esModuleInterop": true,
+    "strict": true,
+    "noEmit": true,
+    "isolatedModules": true,
+    "jsx": "preserve",
+    "types": ["vite/client", "chrome"]
+  },
+  "include": ["src", "vite.config.ts", "tests"]
+}