feat(chat): unread read-receipts with lobby/game dot and history-open ack

Persist per-message read state as a chat_messages.unread_seats bitmask
(migration 00008): a text message seeds every recipient seat's bit, a nudge
only the awaited seat's. A seat's bit clears when the player opens the move
history or chat (POST /games/:id/chat/read, sent only when something is
unread), and a nudge additionally clears when its recipient answers by moving
(a wired game NudgeClearer, dependency-inverted so game keeps off social).

UI shows a per-viewer unread dot in the lobby (next to the opponent) and the
game score bar — the unread_chat game-view flag seeds it from authoritative
REST views, live chat/nudge events raise it. Opening the move history counts
as reading (even without entering chat): the 💬 fade-blinks twice and the
client acks. Admin Messages gains an unread-only filter, a read/unread column,
and a per-message card with the per-seat read breakdown. Observability:
chat_read_duration histogram + chat_unread_messages gauge + social tracing.

gateway/README.md

@@ -52,7 +52,7 @@ out-of-app push to that connector for recipients with no live in-app stream
 
 The message-type catalog: `auth.telegram`, `auth.guest`,
 `auth.email.request`, `auth.email.login`, `profile.get`, `game.submit_play`,
-`game.state`, `lobby.enqueue`, `lobby.poll`, `chat.post` and the play-loop ops;
+`game.state`, `lobby.enqueue`, `lobby.poll`, `chat.post`, `chat.read` and the play-loop ops;
 live events
 `your_turn`, `opponent_moved`, `chat_message`, `nudge`, `match_found` (the game events —
 and `game_over`/`notify` — carry the state delta the client applies without a `game.state`