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/server/dto.go

@@ -112,6 +112,10 @@ type gameDTO struct {
 	// entry (message or nudge) in this game. It seeds the lobby and in-game unread badge.
 	// gameDTOFromGame leaves it false (it has no viewer); the handlers fill it.
 	UnreadChat bool `json:"unread_chat"`
+	// UnreadMessages is a per-viewer flag: at least one of the unread entries is a real chat
+	// message (not just a nudge). It colours the badge — set with UnreadChat it is the regular
+	// badge, UnreadChat alone is the softer nudge-only badge. gameDTOFromGame leaves it false.
+	UnreadMessages bool `json:"unread_messages"`
 }
 
 // moveResultDTO is the outcome of a committed move. Rack carries the actor's refilled rack as

backend/internal/server/handlers_game.go

@@ -443,16 +443,20 @@ func (s *Server) handleListGames(c *gin.Context) {
 		return
 	}
 	memo := map[string]string{}
-	// One query seeds the lobby's per-card unread badge for every listed game.
-	var unread map[uuid.UUID]bool
+	// Two queries seed the lobby's per-card unread badge for every listed game: which games have
+	// any unread entry, and which of those have a real message (so the badge can colour
+	// message-bearing games apart from nudge-only ones).
+	var unread, unreadMsg map[uuid.UUID]bool
 	if s.social != nil {
 		unread, _ = s.social.UnreadGames(c.Request.Context(), uid)
+		unreadMsg, _ = s.social.UnreadMessageGames(c.Request.Context(), uid)
 	}
 	out := make([]gameDTO, 0, len(games))
 	for _, g := range games {
 		dto := gameDTOFromGame(g)
 		s.fillSeatNames(c.Request.Context(), &dto, memo)
 		dto.UnreadChat = unread[g.ID]
+		dto.UnreadMessages = unreadMsg[g.ID]
 		out = append(out, dto)
 	}
 	c.JSON(http.StatusOK, gameListDTO{Games: out, AtGameLimit: atLimit})
@@ -536,8 +540,9 @@ func (s *Server) writeMoveResult(c *gin.Context, res game.MoveResult) {
 	c.JSON(http.StatusOK, dto)
 }
 
-// setUnreadChat fills the per-game unread-chat flag for viewer uid on one game's DTO,
-// when the social domain is present. It is best-effort: a lookup error leaves the flag
+// setUnreadChat fills the per-game unread-chat flags for viewer uid on one game's DTO, when the
+// social domain is present: UnreadChat for any unread entry and UnreadMessages when one of them is
+// a real message (so the badge can be coloured). It is best-effort: a lookup error leaves the flag
 // false (a missing badge) rather than failing the surrounding game response.
 func (s *Server) setUnreadChat(ctx context.Context, g *gameDTO, uid uuid.UUID) {
 	if s.social == nil {
@@ -550,4 +555,7 @@ func (s *Server) setUnreadChat(ctx context.Context, g *gameDTO, uid uuid.UUID) {
 	if unread, err := s.social.HasUnread(ctx, gid, uid); err == nil {
 		g.UnreadChat = unread
 	}
+	if msg, err := s.social.HasUnreadMessage(ctx, gid, uid); err == nil {
+		g.UnreadMessages = msg
+	}
 }