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.

ui/src/lib/model.ts

@@ -47,6 +47,10 @@ export interface GameView {
   lastActivityUnix: number;
   /** true = an honest-AI game: the opponent is shown as 🤖 and chat/nudge/add-friend are disabled. */
   vsAi: boolean;
+  /** Per-viewer flag: the requesting player has at least one unread chat entry (message or
+   *  nudge) in this game. Set on the authoritative REST views (lobby list, game state,
+   *  move result); the live-event GameView leaves it false (events bump unread instead). */
+  unreadChat: boolean;
   seats: Seat[];
 }