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/tests/setup.ts

@@ -0,0 +1,40 @@
+import { vi } from "vitest";
+
+const mockStorage: Record<string, unknown> = {};
+
+vi.stubGlobal("chrome", {
+  runtime: {
+    id: "test-extension-id",
+    onInstalled: {
+      addListener: vi.fn(),
+    },
+    onMessage: {
+      addListener: vi.fn(),
+    },
+    sendMessage: vi.fn(),
+    openOptionsPage: vi.fn(),
+  },
+  storage: {
+    sync: {
+      get: vi.fn((keys: string | string[] | Record<string, unknown>) => {
+        if (typeof keys === "string") {
+          return Promise.resolve({ [keys]: mockStorage[keys] ?? null });
+        }
+        if (Array.isArray(keys)) {
+          const result: Record<string, unknown> = {};
+          for (const key of keys) result[key] = mockStorage[key] ?? null;
+          return Promise.resolve(result);
+        }
+        return Promise.resolve({});
+      }),
+      set: vi.fn((items: Record<string, unknown>) => {
+        Object.assign(mockStorage, items);
+        return Promise.resolve();
+      }),
+    },
+    local: {
+      get: vi.fn(),
+      set: vi.fn(),
+    },
+  },
+});