chore: add katex, dompurify, vitest; copy sample exam files

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/vite.config.ts

@@ -0,0 +1,15 @@
+/// <reference types="vitest" />
+import { defineConfig } from 'vite'
+import react, { reactCompilerPreset } from '@vitejs/plugin-react'
+import babel from '@rolldown/plugin-babel'
+
+export default defineConfig({
+  plugins: [
+    react(),
+    babel({ presets: [reactCompilerPreset()] })
+  ],
+  test: {
+    environment: 'node',
+    globals: true,
+  },
+})