feat(api): add in-memory GameSessionStore

Add the session storage infrastructure for tracking correct answers
during a game. Designed for easy swap to Valkey in Phase 4.

- GameSessionStore interface with create/get/delete methods, all async
  to match the eventual Valkey implementation
- InMemoryGameSessionStore backed by a Map
- GameSessionData holds only the answer key (questionId → correctOptionId)
- Also fix root build script to build packages in dependency order

apps/api/src/gameSessionStore/GameSessionStore.ts

@@ -0,0 +1,7 @@
+export type GameSessionData = { answers: Map<string, number> };
+
+export interface GameSessionStore {
+  create(sessionId: string, data: GameSessionData): Promise<void>;
+  get(sessionId: string): Promise<GameSessionData | null>;
+  delete(sessionId: string): Promise<void>;
+}

apps/api/src/gameSessionStore/InMemoryGameSessionStore.ts

@@ -0,0 +1,17 @@
+import type { GameSessionStore, GameSessionData } from "./GameSessionStore.js";
+
+export class InMemoryGameSessionStore implements GameSessionStore {
+  private sessions = new Map<string, GameSessionData>();
+
+  async create(sessionId: string, data: GameSessionData): Promise<void> {
+    this.sessions.set(sessionId, data);
+  }
+
+  async get(sessionId: string): Promise<GameSessionData | null> {
+    return this.sessions.get(sessionId) ?? null;
+  }
+
+  async delete(sessionId: string): Promise<void> {
+    this.sessions.delete(sessionId);
+  }
+}

apps/api/src/gameSessionStore/index.ts

@@ -0,0 +1,2 @@
+export type { GameSessionStore, GameSessionData } from "./GameSessionStore.js";
+export { InMemoryGameSessionStore } from "./InMemoryGameSessionStore.js";