Bug: Missing online status indicator for match participants when viewed by an unauthenticated user

### Summary

When an unauthenticated user (guest/spectator) views an active match, the presence indicator next to online players shows offline or fails to display correctly.

### Reproduction steps

```bash
1. Start an active match between two players.
2. Open the match page in Incognito mode or as an unauthenticated user (guest).
3. Check the presence indicator next to the players' nicknames.
```

### Expected result

A green status indicator (online) is displayed next to the nicknames of connected active players, regardless of whether the spectator is authenticated.

### Actual result

A gray status indicator (offline) or no indicator is displayed next to the nicknames of active connected participants.

### Browsers

Chrome

### OS

Windows

在 Chrome Incognito 中以未认证访客的身份重现活跃对局页面，并将参与者在线状态指示器与已认证视图进行比较。跟踪参与者的在线状态如何到达对局页面，然后验证已连接的玩家对访客和已登录查看者都显示绿色指示器。

由索引模型根据 Issue 内容生成。