fix: route play-vs-bot to /vs-bot endpoint

POST /api/board/game is @InternalOnly and returns 401 for browser clients.
Switch to /api/board/game/vs-bot which is @PermitAll and notifies the
official-bots service to play the bot side automatically.

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

src/app/services/game-api.service.ts

@@ -40,7 +40,7 @@ export class GameApiService {
         ? { white: playerInfo, black: botInfo }
         : { white: botInfo, black: playerInfo };
 
-    return this.http.post<GameFull>(`${this.apiBase}${this.apiPath}`, payload);
+    return this.http.post<GameFull>(`${this.apiBase}${this.apiPath}/vs-bot`, payload);
   }
 
   getGame(gameId: string): Observable<GameFull> {