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/client.ts

@@ -102,6 +102,9 @@ export interface GatewayClient {
   chatPost(gameId: string, body: string): Promise<ChatMessage>;
   chatList(gameId: string): Promise<ChatMessage[]>;
   nudge(gameId: string): Promise<ChatMessage>;
+  /** Acknowledge the caller has read the game's chat (sent when they open the move history
+   *  or chat), so the backend clears their unread bits and records the read latency. */
+  markChatRead(gameId: string): Promise<void>;
 
   // --- feedback ---
   /** feedbackSubmit sends a feedback message with an optional single attachment. */