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/mock/client.ts

@@ -180,6 +180,7 @@ export class MockGateway implements GatewayClient {
           endReason: '',
           lastActivityUnix: Math.floor(Date.now() / 1000),
           vsAi: true,
+          unreadChat: false,
           seats: [
             { seat: 0, accountId: ME, displayName: 'You', score: 0, hintsUsed: 0, isWinner: false },
             { seat: 1, accountId: 'robot', displayName: 'Robot', score: 0, hintsUsed: 0, isWinner: false },
@@ -211,6 +212,7 @@ export class MockGateway implements GatewayClient {
         endReason: '',
         lastActivityUnix: Math.floor(Date.now() / 1000),
         vsAi: false,
+        unreadChat: false,
         seats: [
           { seat: 0, accountId: ME, displayName: 'You', score: 0, hintsUsed: 0, isWinner: false },
           { seat: 1, accountId: '', displayName: '', score: 0, hintsUsed: 0, isWinner: false },
@@ -487,6 +489,10 @@ export class MockGateway implements GatewayClient {
     this.feedbackReplyUnread = true;
     this.emit({ kind: 'notify', sub: 'admin_reply' });
   }
+  // The mock holds no server-side unread state; the read ack is a no-op (the client clears its
+  // own unread flag optimistically).
+  async markChatRead(): Promise<void> {}
+
   async nudge(gameId: string): Promise<ChatMessage> {
     const g = this.game(gameId);
     const msg: ChatMessage = {