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/robot/driver.go

@@ -152,12 +152,12 @@ func (s *Service) maybeMove(ctx context.Context, rt game.RobotTurn, oppID uuid.U
 	return s.act(ctx, rt, now)
 }
 
-// maybeNudge sends a proactive nudge on a lengthening, randomized schedule (proactiveNudgeGap):
-// the first lands ~60-90 min into the human's turn, and each one waits longer than the last, so a
-// long idle turn gets a handful of increasingly-spaced reminders rather than an hourly stream. The
-// gap is measured from the previous nudge (or the turn start for the first). The social service
-// still enforces the once-per-game floor and rejects a nudge on the robot's own turn, so any such
-// rejection is benign.
+// maybeNudge sends a proactive nudge on a sparse, randomized schedule (proactiveNudgeGap): every
+// nudge waits a uniform random 9-12 h, so a long idle turn gets only a handful of widely-spaced
+// reminders rather than an hourly stream. The gap is measured from the previous nudge (or the turn
+// start for the first). The caller's asleep gate already skips this during the robot's sleep
+// window, so a due nudge fires at the first scan after wake. The social service still enforces the
+// once-per-game floor and rejects a nudge on the robot's own turn, so any such rejection is benign.
 func (s *Service) maybeNudge(ctx context.Context, rt game.RobotTurn, now time.Time) error {
 	ref := rt.TurnStartedAt
 	if last, ok, err := s.social.LastNudgeAt(ctx, rt.GameID, rt.RobotID); err != nil {