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/mock/client.ts

@@ -182,6 +182,7 @@ export class MockGateway implements GatewayClient {
           lastActivityUnix: Math.floor(Date.now() / 1000),
           vsAi: true,
           unreadChat: false,
+          unreadMessages: false,
           seats: [
             { seat: 0, accountId: ME, displayName: 'You', score: 0, hintsUsed: 0, isWinner: false },
             { seat: 1, accountId: 'robot', displayName: 'Robot', score: 0, hintsUsed: 0, isWinner: false },
@@ -214,6 +215,7 @@ export class MockGateway implements GatewayClient {
         lastActivityUnix: Math.floor(Date.now() / 1000),
         vsAi: false,
         unreadChat: false,
+        unreadMessages: false,
         seats: [
           { seat: 0, accountId: ME, displayName: 'You', score: 0, hintsUsed: 0, isWinner: false },
           { seat: 1, accountId: '', displayName: '', score: 0, hintsUsed: 0, isWinner: false },

ui/src/lib/mock/data.ts

@@ -181,6 +181,7 @@ function activeGame(): MockGame {
       dictVersion: 'v1',
       vsAi: false,
       unreadChat: false,
+      unreadMessages: false,
       status: 'active',
       players: 2,
       toMove: 0,
@@ -218,6 +219,7 @@ function finishedG2(): MockGame {
       dictVersion: 'v1',
       vsAi: false,
       unreadChat: false,
+      unreadMessages: false,
       status: 'finished',
       players: 2,
       toMove: 0,
@@ -256,6 +258,7 @@ function finishedG3(): MockGame {
       dictVersion: 'v1',
       vsAi: false,
       unreadChat: false,
+      unreadMessages: false,
       status: 'finished',
       players: 2,
       toMove: 0,