feat: sparser robot nudges, typed unread badge, lobby unread bump

Three owner-requested polish changes:

- robot: replace the lengthening 60-90 min -> 6 h proactive-nudge ramp with a
  flat uniform 9-12 h wait before every nudge; the existing sleep-window gate
  still skips and defers a nudge that would land in the robot's night.
- ui: colour the lobby/in-game unread dot by type -- the regular danger colour
  when a chat message is unread, a softer amber (--warn) when only nudges are.
  Adds a per-viewer unread_messages flag (chat_messages.kind='message') across
  the backend DTO, FlatBuffers wire, gateway transcode and the UI store.
- ui: float games with any unread notification to the top of the lobby's
  your-turn and opponent-turn sections (finished keeps its order), reusing the
  existing unread_chat flag.

Docs (ARCHITECTURE 7, FUNCTIONAL + _ru) updated. No DB migration; the new wire
field is backward-compatible.

ui/src/game/Game.svelte

@@ -14,6 +14,7 @@
   import { t, type MessageKey } from '../lib/i18n/index.svelte';
   import type { EvalResult, MoveRecord, MoveResult, StateView, Tile } from '../lib/model';
   import { lastMoveCells, replay } from '../lib/board';
+  import { badgeKind } from '../lib/unread';
   import { historyGrid } from '../lib/history';
   import { centre, premiumGrid } from '../lib/premiums';
   import { variantNameKey } from '../lib/variants';
@@ -183,7 +184,7 @@
       view = st;
       syncWallet(st.walletBalance);
       // Seed the unread flag from the authoritative state (the live stream only raises it).
-      seedChatUnread(id, st.game.unreadChat);
+      seedChatUnread(id, st.game.unreadChat, st.game.unreadMessages);
       moves = hist.moves;
       setCachedGame(id, st, hist.moves, draft);
       // Mirror the fresh status into the lobby snapshot so returning there shows it without a
@@ -670,7 +671,7 @@
     };
     // The move result is an authoritative per-viewer view: a nudge the actor just answered by
     // moving is already cleared server-side, so reconcile the unread flag from it.
-    seedChatUnread(id, r.game.unreadChat);
+    seedChatUnread(id, r.game.unreadChat, r.game.unreadMessages);
     moves = [...moves, r.move];
     // A committed move clears the actor's draft on the server, so clear the cached draft too;
     // otherwise a same-session re-entry would briefly re-apply the now-stale composition.
@@ -1091,10 +1092,11 @@
      above so the markup and logic stay single-sourced (see the {#if landscape} split). -->
 {#snippet scoreboardBlock()}
   {#if view}
+    {@const badge = badgeKind(app.chatUnread[id] ?? false, app.messageUnread[id] ?? false)}
     <!-- svelte-ignore a11y_no_static_element_interactions -->
     <!-- svelte-ignore a11y_click_events_have_key_events -->
     <div class="scoreboard" class:flat={landscape} onclick={landscape ? undefined : toggleHistory}>
-      {#if app.chatUnread[id]}<span class="unread-dot sbadge-dot"></span>{/if}
+      {#if badge}<span class="unread-dot sbadge-dot" class:nudge={badge === 'nudge'}></span>{/if}
       {#each view.game.seats as s (s.seat)}
         <div class="seat" class:turn={view.game.toMove === s.seat && !gameOver} class:win={s.isWinner}>
           <div class="nm" class:struck={seatBlocked(s)}>{seatName(s)}</div>
@@ -1582,13 +1584,17 @@
     color: var(--danger);
   }
   /* The unread-chat dot on the score bar's corner; the history's 💬 icon fade-blinks (two cycles)
-     when the history is opened with unread present, rather than carrying a count badge. */
+     when the history is opened with unread present, rather than carrying a count badge. Red for an
+     unread message, a softer amber when only nudges are unread. */
   .unread-dot {
     width: 8px;
     height: 8px;
     border-radius: 50%;
     background: var(--danger);
   }
+  .unread-dot.nudge {
+    background: var(--warn);
+  }
   .sbadge-dot {
     position: absolute;
     top: 4px;