feat(api): add answer evaluation endpoint

Complete the game answer flow:

- Add evaluateAnswer service function: looks up the session in the
  GameSessionStore, compares the submitted optionId against the stored
  correct answer, returns an AnswerResult.
- Add submitAnswer controller with safeParse validation and error
  handling (session/question not found → 404).
- Add POST /api/v1/game/answer route.
- Fix createGameSession: was missing the answerKey tracking and the
  gameSessionStore.create() call, so sessions were never persisted.

The full singleplayer game loop now works end-to-end:
POST /game/start → GameSession, POST /game/answer → AnswerResult.

apps/api/src/controllers/gameController.ts

@@ -1,6 +1,6 @@
 import type { Request, Response } from "express";
-import { GameRequestSchema } from "@glossa/shared";
-import { createGameSession } from "../services/gameService.js";
+import { GameRequestSchema, AnswerSubmissionSchema } from "@glossa/shared";
+import { createGameSession, evaluateAnswer } from "../services/gameService.js";
 
 export const createGame = async (req: Request, res: Response) => {
   const gameSettings = GameRequestSchema.safeParse(req.body);
@@ -15,3 +15,18 @@ export const createGame = async (req: Request, res: Response) => {
 
   res.json({ success: true, data: gameQuestions });
 };
+
+export const submitAnswer = async (req: Request, res: Response) => {
+  const submission = AnswerSubmissionSchema.safeParse(req.body);
+  // TODO: remove when global error handler is implemented
+  if (!submission.success) {
+    res.status(400).json({ success: false });
+    return;
+  }
+  try {
+    const result = await evaluateAnswer(submission.data);
+    res.json({ success: true, data: result });
+  } catch (error) {
+    res.status(404).json({ success: false });
+  }
+};