feat(hint): idle-gated wallet-free vs_ai hint on a monotonic clock (B4)

A vs_ai hint is now unlimited and wallet-free, but idle-gated as an anti-frustration
aid: it unlocks only after the player has been stuck ~30 min on a turn (timed from the
robot's last move; the human's first move, before the robot has played, is exempt).
While gated the hint button carries a small lock badge and a tap shows the remaining
minutes ('Available in N min.'); the lock lifts live at the mark.

The gate is enforced CLIENT-SIDE against a MONOTONIC clock (performance.now()), never a
wall-clock timestamp: a device clock the player controls (or an auto-sync) must not be
able to open or freeze it. The wait is therefore session-scoped -- a reload restarts it
(there is no tamper-proof way to carry idle time across a relaunch without a wall clock).
An online vs_ai game will gate the same way but from the server's clock (a follow-up).

- lib/hints.ts: HINT_GATE_MS + pure hintGateRemainingMs (monotonic) + hintLockMinutes;
  removed the wall-clock hintRemainingMs. Unit-tested red->green.
- Game.svelte: the monotonic gate (hintGateStart/monoNow, armed on the turn change), a
  vs_ai hint button (plain: no confirm, no count; lock badge + gated tap -> toast), a
  live 10s tick.
- localgame: removed the wall-clock hint gate and the now-dead robotLastMoveAtUnix field
  from source.ts/serialize.ts (the client is authoritative); hint() just serves the top
  move.
- i18n game.hintLockedIn.
- offline.spec.ts: assert the first move is un-gated and the lock arms after the robot moves.
- Docs FUNCTIONAL(+_ru) + ARCHITECTURE; bundle budget 114->115 (game-screen feature).

ui/src/lib/localgame/source.ts

@@ -34,9 +34,6 @@ import type { Move } from '../dict/validate';
 
 export { LOCAL_ID_PREFIX, isLocalGameId };
 
-/** HINT_GATE_MS is the idle time since the robot's last move before an offline hint unlocks. */
-export const HINT_GATE_MS = 30 * 60 * 1000;
-
 /**
  * GameLoopSource is the subset of GatewayClient the game screen calls to run a game. The real
  * gateway satisfies it structurally; the local source implements it for offline play.
@@ -123,7 +120,6 @@ export class LocalSource implements GameLoopSource {
       seats: opts.seats.map((s) => ({ kind: s.kind, name: s.name, accountId: s.accountId })),
       createdAtUnix: now,
       updatedAtUnix: now,
-      robotLastMoveAtUnix: now,
     });
     const entry: Live = { game, record };
     this.live.set(opts.id, entry);
@@ -191,10 +187,10 @@ export class LocalSource implements GameLoopSource {
   }
 
   async hint(gameId: string): Promise<HintResult> {
+    // The idle gate is enforced client-side with a monotonic clock (see Game.svelte / lib/hints):
+    // a wall-clock timestamp here could be defeated by changing the device clock. This just serves
+    // the engine's top-ranked move; the client only calls it once the gate is open.
     const entry = await this.load(gameId);
-    if (nowUnix() * 1000 - entry.record.robotLastMoveAtUnix * 1000 < HINT_GATE_MS) {
-      throw new GatewayError('hint_not_ready');
-    }
     const top = this.topMove(entry.game);
     if (!top) throw new GatewayError('no_hint');
     return { move: this.moveFromGen(entry.record.variant, entry.game.currentPlayer, top), hintsRemaining: 1, walletBalance: 0 };
@@ -280,7 +276,6 @@ export class LocalSource implements GameLoopSource {
       if (dec.kind === 'play') out.push(g.play(dec.move.dir, dec.move.tiles));
       else if (dec.kind === 'exchange' && g.bagLength >= RULESETS[entry.record.variant].rackSize) out.push(g.exchange(dec.exchange));
       else out.push(g.pass());
-      entry.record.robotLastMoveAtUnix = nowUnix();
     }
     return out;
   }
@@ -306,7 +301,6 @@ export class LocalSource implements GameLoopSource {
       seats: entry.record.seats,
       createdAtUnix: entry.record.createdAtUnix,
       updatedAtUnix: nowUnix(),
-      robotLastMoveAtUnix: entry.record.robotLastMoveAtUnix,
     });
     await saveLocalGame(entry.record);
   }