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/unread.test.ts

@@ -0,0 +1,18 @@
+import { describe, expect, it } from 'vitest';
+import { badgeKind } from './unread';
+
+describe('badgeKind', () => {
+  it('shows nothing when nothing is unread', () => {
+    expect(badgeKind(false, false)).toBeNull();
+    // message without unread is inconsistent input; the unread guard still wins.
+    expect(badgeKind(false, true)).toBeNull();
+  });
+
+  it('is a nudge badge when only nudges are unread', () => {
+    expect(badgeKind(true, false)).toBe('nudge');
+  });
+
+  it('is a message badge when a real message is unread', () => {
+    expect(badgeKind(true, true)).toBe('message');
+  });
+});