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/chatread_test.go

@@ -16,7 +16,8 @@ import (
 )
 
 // TestChatUnreadAndMarkRead checks a text message marks every recipient seat unread (not the
-// sender), surfaces through HasUnread / UnreadGames, and that MarkRead clears the reader's bit.
+// sender), surfaces through HasUnread / UnreadGames and the message-level HasUnreadMessage /
+// UnreadMessageGames (it is a real message, not a nudge), and that MarkRead clears the reader's bit.
 func TestChatUnreadAndMarkRead(t *testing.T) {
 	ctx := context.Background()
 	svc := newSocialService()
@@ -37,6 +38,15 @@ func TestChatUnreadAndMarkRead(t *testing.T) {
 	} else if !set[gameID] {
 		t.Error("UnreadGames should include the game for the recipient")
 	}
+	// A text message also raises the message-level flags (it is not just a nudge).
+	if msg, _ := svc.HasUnreadMessage(ctx, gameID, seats[1]); !msg {
+		t.Error("recipient should have the message flagged as an unread message")
+	}
+	if set, err := svc.UnreadMessageGames(ctx, seats[1]); err != nil {
+		t.Fatalf("unread message games: %v", err)
+	} else if !set[gameID] {
+		t.Error("UnreadMessageGames should include the game for a text message")
+	}
 
 	// Reading it clears the recipient's bit and reports one entry marked.
 	if n, err := svc.MarkRead(ctx, gameID, seats[1]); err != nil {
@@ -55,7 +65,8 @@ func TestChatUnreadAndMarkRead(t *testing.T) {
 
 // TestNudgeUnreadTargetsOnlyToMove checks, in a three-player game, that a nudge marks ONLY the
 // awaited (to-move) seat unread — never the other waiting players. This is the owner's nudge
-// targeting invariant, now observable through the unread bitmask.
+// targeting invariant, now observable through the unread bitmask. It also checks a nudge raises
+// HasUnread but not the message-level flags, so the badge can colour it apart from a real message.
 func TestNudgeUnreadTargetsOnlyToMove(t *testing.T) {
 	ctx := context.Background()
 	svc := newSocialService()
@@ -68,6 +79,13 @@ func TestNudgeUnreadTargetsOnlyToMove(t *testing.T) {
 	if unread, _ := svc.HasUnread(ctx, gameID, seats[0]); !unread {
 		t.Error("the awaited seat should have the nudge unread")
 	}
+	// A nudge is not a message: it must not raise the message-level flags.
+	if msg, _ := svc.HasUnreadMessage(ctx, gameID, seats[0]); msg {
+		t.Error("a nudge must not be flagged as an unread message")
+	}
+	if set, _ := svc.UnreadMessageGames(ctx, seats[0]); set[gameID] {
+		t.Error("UnreadMessageGames must not include a game whose only unread entry is a nudge")
+	}
 	if unread, _ := svc.HasUnread(ctx, gameID, seats[2]); unread {
 		t.Error("a non-awaited waiting seat must not receive the nudge")
 	}