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/lib/app.svelte.ts

@@ -63,6 +63,10 @@ export const app = $state<{
    *  game, for the lobby and in-game unread dot. Seeded from the authoritative REST views and
    *  raised by live chat/nudge events; cleared (with a backend ack) on opening the history/chat. */
   chatUnread: Record<string, boolean>;
+  /** Per-game flag: at least one unread entry is a real message (not just a nudge), so the dot
+   *  can be coloured apart from the nudge-only case. Same lifecycle as chatUnread; nudge events
+   *  raise only chatUnread, message events raise both. */
+  messageUnread: Record<string, boolean>;
   /** Whether an operator feedback reply awaits the player, for the lobby ⚙️ badge (combined
    *  with friend requests) and the Settings → Info badge. */
   feedbackReplyUnread: boolean;
@@ -93,6 +97,7 @@ export const app = $state<{
   localeLocked: false,
   notifications: 0,
   chatUnread: {},
+  messageUnread: {},
   feedbackReplyUnread: false,
   staleInvite: false,
   welcomeRedeem: false,
@@ -170,14 +175,18 @@ export function dismissWelcomeRedeem(): void {
 }
 
 /**
- * seedChatUnread sets a game's unread flag from an authoritative per-viewer REST view (the lobby
- * list, a game's state, or a move result). The live-event GameView omits the flag, so the live
- * stream raises unread (bumpChatUnread) rather than seeding it from a GameView.
+ * seedChatUnread sets a game's unread flags from an authoritative per-viewer REST view (the lobby
+ * list, a game's state, or a move result): unread is any unread entry, message whether one of them
+ * is a real message (the badge colour). The live-event GameView omits both, so the live stream
+ * raises them on receive rather than seeding from a GameView.
  */
-export function seedChatUnread(gameId: string, unread: boolean): void {
+export function seedChatUnread(gameId: string, unread: boolean, message: boolean): void {
   if ((app.chatUnread[gameId] ?? false) !== unread) {
     app.chatUnread = { ...app.chatUnread, [gameId]: unread };
   }
+  if ((app.messageUnread[gameId] ?? false) !== message) {
+    app.messageUnread = { ...app.messageUnread, [gameId]: message };
+  }
 }
 
 /**
@@ -192,6 +201,7 @@ export function seedChatUnread(gameId: string, unread: boolean): void {
 export function markChatRead(gameId: string): void {
   if (!app.chatUnread[gameId]) return;
   app.chatUnread = { ...app.chatUnread, [gameId]: false };
+  if (app.messageUnread[gameId]) app.messageUnread = { ...app.messageUnread, [gameId]: false };
   void gateway.markChatRead(gameId).catch(() => {});
 }
 
@@ -262,6 +272,11 @@ function openStream(): void {
           router.route.params.id === e.message.gameId;
         if (!inComms) {
           app.chatUnread = { ...app.chatUnread, [e.message.gameId]: true };
+          // Only a real message colours the badge; a nudge delivered as a chat_message must not
+          // raise the message flag (the separate nudge event below also leaves it untouched).
+          if (e.message.kind !== 'nudge') {
+            app.messageUnread = { ...app.messageUnread, [e.message.gameId]: true };
+          }
           showToast(e.message.kind === 'nudge' ? t('chat.nudge') : e.message.body, 'info');
         }
       } else if (e.kind === 'nudge') {