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.ts

@@ -0,0 +1,17 @@
+// Pure resolution of the per-game unread dot's kind, kept out of the .svelte components so it can
+// be unit-tested. A game's dot is shown when anything is unread; its colour distinguishes a real
+// chat message (the regular danger colour) from nudge-only unread (a softer nudge colour).
+
+/** BadgeKind is the unread dot to show for a game, or null when nothing is unread. */
+export type BadgeKind = 'message' | 'nudge' | null;
+
+/**
+ * badgeKind picks the unread dot for a game from its two per-viewer flags: null when nothing is
+ * unread, 'message' when an unread real chat message is present (the regular colour), else 'nudge'
+ * when only nudges are unread (the softer colour). message implies unread, so a stray message=true
+ * with unread=false still shows nothing.
+ */
+export function badgeKind(unread: boolean, message: boolean): BadgeKind {
+  if (!unread) return null;
+  return message ? 'message' : 'nudge';
+}