feat(hint): persist the vs_ai idle-hint wait (wall-clock + read sanitiser)

Per the owner's call, the idle-hint gate now PERSISTS across leaving and reopening the
app, instead of the session-scoped monotonic clock: the unlock is a wall-clock instant
(hintUnlockAtMs) stamped from the robot's reply, stored on the local record, carried on
the game view + the opponent_moved move delta, and read through a sanitiser that caps it
at now + the window. So:
- the wait survives a relaunch (a stuck turn is not forgotten);
- a device clock set BACK cannot freeze the gate (the cap bounds the remaining to the
  window and self-heals on the next read);
- a clock set FORWARD just opens the hint early -- accepted as harmless for a solo game.

- lib/hints.ts hintGateRemainingMs now takes the unlock instant + clamps to the window.
- localgame: re-add hintUnlockAtMs to the record/meta; stamp it off the robot's reply;
  sanitise on read (a shared hintUnlock helper feeds stateView + the opponent_moved event).
- gamedelta + PushEvent: the move delta carries hintUnlockAtMs so the view stays fresh.
- Game.svelte: hintUnlockAt derives from the view; the tick + lock + toast unchanged.
- offline.spec.ts: also assert the lock survives a reload (the wait persisted).
- Docs FUNCTIONAL(+_ru)/ARCHITECTURE updated (persist + sanitiser, not monotonic-resets).

ui/src/lib/localgame/serialize.ts

@@ -38,6 +38,11 @@ export interface LocalGameRecord {
   status: 'active' | 'finished';
   createdAtUnix: number;
   updatedAtUnix: number;
+  /** Wall-clock ms at which the vs_ai idle hint unlocks (the robot's last move + the window), or 0
+   *  while open (no robot move yet). Persisted so the wait survives leaving and reopening the app;
+   *  read through a sanitiser (cap at now + window) so a device clock set back cannot freeze it —
+   *  see lib/hints. */
+  hintUnlockAtMs: number;
 }
 
 /** The record fields the caller owns (the engine supplies the rest). */
@@ -46,6 +51,7 @@ export interface RecordMeta {
   seats: Seat[];
   createdAtUnix: number;
   updatedAtUnix: number;
+  hintUnlockAtMs: number;
 }
 
 /**
@@ -67,6 +73,7 @@ export function serializeGame(game: LocalGame, meta: RecordMeta): LocalGameRecor
     status: game.isOver ? 'finished' : 'active',
     createdAtUnix: meta.createdAtUnix,
     updatedAtUnix: meta.updatedAtUnix,
+    hintUnlockAtMs: meta.hintUnlockAtMs,
   };
 }