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.

documentation/api-development.md

@@ -298,3 +298,7 @@ Required before: implementing the double join for source language prompt.
   `buildSession()`.
 - **Session statefulness:** game loop is currently stateless (fetch all questions upfront).
   Confirm this is still the intended MVP approach before building `buildSession()`.
+- **Glosses can leak answers:** some WordNet glosses contain the target-language
+  word in the definition text (e.g. "Padre" appearing in the English gloss for
+  "father"). Address during the post-MVP data enrichment pass — either clean the
+  glosses, replace them with custom definitions, or filter at the service layer.