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

web/src/server/api/schemas/extension.ts

@@ -0,0 +1,15 @@
+import { object, string, optional } from "valibot";
+
+export const GetAuthStatusSchema = object({
+  apiKey: optional(string()),
+});
+
+export const LinkDeviceSchema = object({
+  extensionId: string(),
+  deviceName: optional(string()),
+});
+
+export const ReportPhishingSchema = object({
+  url: string(),
+  source: optional(string()),
+});