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/vite.config.ts

@@ -0,0 +1,24 @@
+import { defineConfig } from "vite";
+import { resolve } from "path";
+import { fileURLToPath } from "url";
+
+const __dirname = fileURLToPath(new URL(".", import.meta.url));
+
+export default defineConfig({
+  build: {
+    outDir: "dist",
+    emptyOutDir: true,
+    rollupOptions: {
+      input: {
+        background: resolve(__dirname, "src/background/index.ts"),
+        content: resolve(__dirname, "src/content/index.ts"),
+        popup: resolve(__dirname, "src/popup/popup.html"),
+        options: resolve(__dirname, "src/options/options.html"),
+      },
+      output: {
+        entryFileNames: "[name].js",
+      },
+    },
+  },
+  publicDir: "public",
+});