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/inttest/robot_test.go

@@ -181,8 +181,8 @@ func TestMatchmakerSubstitutesRobotEndToEnd(t *testing.T) {
 	}
 }
 
-// TestRobotProactiveNudge checks the robot's lengthening proactive-nudge schedule on the
-// human's turn: nothing before the ~60-90 min first gap, exactly one once it has elapsed.
+// TestRobotProactiveNudge checks the robot's flat proactive-nudge schedule on the human's
+// turn: nothing before the 9 h floor of the 9-12 h gap, exactly one once past its 12 h ceiling.
 func TestRobotProactiveNudge(t *testing.T) {
 	ctx := context.Background()
 	svc := newGameService()
@@ -206,18 +206,20 @@ func TestRobotProactiveNudge(t *testing.T) {
 		t.Fatalf("create: %v", err)
 	}
 
-	// A daytime turn start (the robot is awake for every ±3h drift between 07:30 and 12:00). No
-	// nudge before the 60-min floor of the first gap; exactly one once past its 90-min ceiling.
-	start := time.Date(2024, 1, 1, 10, 0, 0, 0, time.UTC)
+	// A noon turn start. The drive instants below sit at UTC hours 20:00 and (next day) 12:00,
+	// both in [10:00, 20:00] so the robot is awake for every ±3h sleep drift — the gap, not the
+	// sleep window, decides the outcome. No nudge at 8 h idle (before the 9 h floor); exactly one
+	// at 24 h idle (well past the 12 h ceiling, however the seed drew within 9-12 h).
+	start := time.Date(2024, 1, 1, 12, 0, 0, 0, time.UTC)
 	setTurnStarted(t, g.ID, start)
 
-	robots.Drive(ctx, start.Add(30*time.Minute))
+	robots.Drive(ctx, start.Add(8*time.Hour))
 	if n := countNudges(t, g.ID, robotID); n != 0 {
-		t.Errorf("robot nudges = %d at 30m idle, want 0 (before the first gap)", n)
+		t.Errorf("robot nudges = %d at 8h idle, want 0 (before the 9h floor)", n)
 	}
-	robots.Drive(ctx, start.Add(2*time.Hour))
+	robots.Drive(ctx, start.Add(24*time.Hour))
 	if n := countNudges(t, g.ID, robotID); n != 1 {
-		t.Errorf("robot nudges = %d at 2h idle, want 1 (after the first gap)", n)
+		t.Errorf("robot nudges = %d at 24h idle, want 1 (past the 12h ceiling)", n)
 	}
 }