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/screens/Lobby.svelte

@@ -3,7 +3,7 @@
   import { SvelteMap, SvelteSet } from 'svelte/reactivity';
   import Screen from '../components/Screen.svelte';
   import TabBar from '../components/TabBar.svelte';
-  import { app, handleError, refreshFeedbackBadge } from '../lib/app.svelte';
+  import { app, handleError, refreshFeedbackBadge, seedChatUnread } from '../lib/app.svelte';
   import { connection } from '../lib/connection.svelte';
   import { gateway } from '../lib/gateway';
   import { navigate } from '../lib/router.svelte';
@@ -33,6 +33,9 @@
     try {
       const list = await gateway.gamesList();
       games = list.games;
+      // Seed the per-game unread badges from the authoritative list. The live stream only raises
+      // unread (it never seeds it from a GameView), so a persisted unread survives a reload here.
+      for (const g of games) seedChatUnread(g.id, g.unreadChat);
       atGameLimit = list.atGameLimit;
       if (!guest) {
         [invitations, incoming] = await Promise.all([gateway.invitationsList(), gateway.friendsIncoming()]);
@@ -262,7 +265,10 @@
                     onclick={() => openGame(g)}
                   >
                     <span class="info">
-                      <span class="who">{opponents(g) || '—'}</span>
+                      <span class="who">
+                        <span class="who-name">{opponents(g) || '—'}</span>
+                        {#if app.chatUnread[g.id]}<span class="unread-dot"></span>{/if}
+                      </span>
                       <span class="sub">{scoreline(g)}</span>
                     </span>
                     <!-- Re-key on the per-card blink nonce so a repeat blink restarts the fade. -->
@@ -441,11 +447,25 @@
     min-width: 0;
   }
   .who {
+    display: flex;
+    align-items: center;
+    gap: 6px;
+    min-width: 0;
     font-weight: 600;
+  }
+  .who-name {
     white-space: nowrap;
     overflow: hidden;
     text-overflow: ellipsis;
   }
+  /* A small red dot beside the opponent name: this game has an unread chat entry. */
+  .unread-dot {
+    flex: 0 0 auto;
+    width: 8px;
+    height: 8px;
+    border-radius: 50%;
+    background: var(--danger);
+  }
   .sub {
     font-size: 0.85rem;
     color: var(--text-muted);