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

Reproduce the active match page as an unauthenticated guest in Chrome Incognito and compare the participant presence indicator with an authenticated view. Trace how participant online status reaches the match page, then verify that connected players show a green indicator for guests as well as signed-in viewers.

索引モデルが issue の本文から書いたものです。