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.

gateway/internal/transcode/encode.go

@@ -441,6 +441,7 @@ func toWireGame(g backendclient.GameResp) wire.GameView {
 		Seats:                seats,
 		LastActivityUnix:     g.LastActivityUnix,
 		UnreadChat:           g.UnreadChat,
+		UnreadMessages:       g.UnreadMessages,
 	}
 }
 

gateway/internal/transcode/transcode_test.go

@@ -254,7 +254,7 @@ func TestGamesListRoundTripDecodesSeatNames(t *testing.T) {
 		if r.URL.Path != "/api/v1/user/games" {
 			t.Errorf("unexpected path %q", r.URL.Path)
 		}
-		_, _ = w.Write([]byte(`{"games":[{"id":"g-1","variant":"scrabble_en","status":"active","players":2,"to_move":0,"last_activity_unix":1717000000,"unread_chat":true,"seats":[{"seat":0,"account_id":"u-9","display_name":"You","score":10},{"seat":1,"account_id":"a-1","display_name":"Ann","score":7}]}],"at_game_limit":true}`))
+		_, _ = w.Write([]byte(`{"games":[{"id":"g-1","variant":"scrabble_en","status":"active","players":2,"to_move":0,"last_activity_unix":1717000000,"unread_chat":true,"unread_messages":true,"seats":[{"seat":0,"account_id":"u-9","display_name":"You","score":10},{"seat":1,"account_id":"a-1","display_name":"Ann","score":7}]}],"at_game_limit":true}`))
 	})
 	defer cleanup()
 
@@ -279,6 +279,9 @@ func TestGamesListRoundTripDecodesSeatNames(t *testing.T) {
 	if !g.UnreadChat() {
 		t.Error("unread_chat = false, want true (the backend flagged unread for the viewer)")
 	}
+	if !g.UnreadMessages() {
+		t.Error("unread_messages = false, want true (the backend flagged an unread message)")
+	}
 	var seat fb.SeatView
 	g.Seats(&seat, 1)
 	if string(seat.DisplayName()) != "Ann" {