feat(web): add minimal playable quiz at /play

- Add Vite proxy for /api → localhost:3000 (no CORS needed in dev)
- Create /play route with hardcoded game settings (en→it, nouns, easy)
- Three-phase state machine: loading → playing → finished
- Show prompt, optional gloss, and 4 answer buttons per question
- Submit answers to /api/v1/game/answer, show correct/wrong feedback
- Manual Next button to advance after answering
- Score screen on completion
- Add selectedOptionId to AnswerResult schema (discovered during
  frontend work that the result needs to be self-contained for
  rendering feedback without separate client state)

Intentionally unstyled — component extraction and polish come next.

apps/web/vite.config.ts

@@ -10,4 +10,5 @@ export default defineConfig({
     react(),
     tailwindcss(),
   ],
+  server: { proxy: { "/api": "http://localhost:3000" } },
 });