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.

ui/src/lib/lobbysort.ts

@@ -43,11 +43,16 @@ export interface LobbyGroups {
 }
 
 /**
- * groupGames partitions games for myId into the three lobby sections and orders each: the
- * your-turn games by ascending last activity (the longest-waiting first), the opponent-turn
- * and finished games by descending last activity (the most recent first).
+ * groupGames partitions games for myId into the three lobby sections and orders each. In the two
+ * active sections a game with an unread notification (unread[g.id], any chat entry or nudge) sorts
+ * first, then by last activity: your-turn ascending (the longest-waiting first), opponent-turn
+ * descending (the most recent first). Finished games ignore unread and stay descending by activity.
  */
-export function groupGames(games: GameView[], myId: string): LobbyGroups {
+export function groupGames(
+  games: GameView[],
+  myId: string,
+  unread: Record<string, boolean>,
+): LobbyGroups {
   const yourTurn: GameView[] = [];
   const theirTurn: GameView[] = [];
   const finished: GameView[] = [];
@@ -56,8 +61,10 @@ export function groupGames(games: GameView[], myId: string): LobbyGroups {
     else if (isMyTurn(g, myId)) yourTurn.push(g);
     else theirTurn.push(g);
   }
-  yourTurn.sort((a, b) => a.lastActivityUnix - b.lastActivityUnix);
-  theirTurn.sort((a, b) => b.lastActivityUnix - a.lastActivityUnix);
+  // Unread is the primary key in the active sections (rank 1 before rank 0), last activity the tie-break.
+  const rank = (g: GameView) => (unread[g.id] ? 1 : 0);
+  yourTurn.sort((a, b) => rank(b) - rank(a) || a.lastActivityUnix - b.lastActivityUnix);
+  theirTurn.sort((a, b) => rank(b) - rank(a) || b.lastActivityUnix - a.lastActivityUnix);
   finished.sort((a, b) => b.lastActivityUnix - a.lastActivityUnix);
   return { yourTurn, theirTurn, finished };
 }