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.

backend/internal/social/chatread.go

@@ -67,6 +67,21 @@ func (svc *Service) HasUnread(ctx context.Context, gameID, viewerID uuid.UUID) (
 	return svc.store.hasUnread(ctx, gameID, viewerID)
 }
 
+// UnreadMessageGames returns the subset of UnreadGames whose unread entries include a real chat
+// message (a 'message' kind, not a nudge), for colouring the lobby's per-card unread badge: a game
+// present here has an unread message (the regular badge), one only in UnreadGames has nudges alone
+// (the soft nudge badge).
+func (svc *Service) UnreadMessageGames(ctx context.Context, viewerID uuid.UUID) (map[uuid.UUID]bool, error) {
+	return svc.store.unreadMessageGames(ctx, viewerID)
+}
+
+// HasUnreadMessage reports whether viewerID has an unread chat message (a 'message' kind, not a
+// nudge) in the game, for distinguishing a message badge from a nudge-only one on a single game's
+// state and move-result views.
+func (svc *Service) HasUnreadMessage(ctx context.Context, gameID, viewerID uuid.UUID) (bool, error) {
+	return svc.store.hasUnreadMessage(ctx, gameID, viewerID)
+}
+
 // readMark is one chat entry that flipped from unread to read, carrying what the
 // publish-to-read latency metric needs.
 type readMark struct {
@@ -161,6 +176,43 @@ func (s *Store) hasUnread(ctx context.Context, gameID, viewerID uuid.UUID) (bool
 	return ok, nil
 }
 
+// unreadMessageGames is unreadGames restricted to real chat messages (kind 'message', not a
+// nudge), so the caller can tell a message badge from a nudge-only one in one extra query.
+func (s *Store) unreadMessageGames(ctx context.Context, viewerID uuid.UUID) (map[uuid.UUID]bool, error) {
+	const q = `SELECT DISTINCT m.game_id
+FROM backend.chat_messages m
+JOIN backend.game_players p ON p.game_id = m.game_id AND p.account_id = $1
+WHERE m.kind = 'message' AND m.unread_seats <> 0 AND (m.unread_seats::int & (1 << p.seat::int)) <> 0`
+	rows, err := s.db.QueryContext(ctx, q, viewerID)
+	if err != nil {
+		return nil, fmt.Errorf("social: unread message games: %w", err)
+	}
+	defer rows.Close()
+	out := make(map[uuid.UUID]bool)
+	for rows.Next() {
+		var id uuid.UUID
+		if err := rows.Scan(&id); err != nil {
+			return nil, fmt.Errorf("social: scan unread message games: %w", err)
+		}
+		out[id] = true
+	}
+	return out, rows.Err()
+}
+
+// hasUnreadMessage reports whether viewerID has an unread real chat message (kind 'message', not
+// a nudge) in the one game.
+func (s *Store) hasUnreadMessage(ctx context.Context, gameID, viewerID uuid.UUID) (bool, error) {
+	const q = `SELECT EXISTS(
+  SELECT 1 FROM backend.chat_messages m
+  JOIN backend.game_players p ON p.game_id = m.game_id AND p.account_id = $2
+  WHERE m.game_id = $1 AND m.kind = 'message' AND (m.unread_seats::int & (1 << p.seat::int)) <> 0)`
+	var ok bool
+	if err := s.db.QueryRowContext(ctx, q, gameID, viewerID).Scan(&ok); err != nil {
+		return false, fmt.Errorf("social: has unread message: %w", err)
+	}
+	return ok, nil
+}
+
 // countUnread counts the chat entries with at least one recipient seat still unread,
 // for the chat_unread_messages gauge.
 func (s *Store) countUnread(ctx context.Context) (int64, error) {