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/e2e/offline.spec.ts

@@ -60,6 +60,9 @@ test.describe('offline mode', () => {
     await page.locator('button.invite').click();
     await expect(page.locator('[data-cell]').first()).toBeVisible();
 
+    // The human's first move is not idle-gated: the hint is available at once (no 🔒 lock badge).
+    await expect(page.locator('.lock')).toHaveCount(0);
+
     // The human plays WAY horizontally across the centre (7,5)-(7,7).
     await placeTile(page, 'W', 7, 5);
     await placeTile(page, 'A', 7, 6);
@@ -74,6 +77,10 @@ test.describe('offline mode', () => {
     }).toPass({ timeout: 15000 });
     const filled = await page.locator('[data-cell].filled').count();
 
+    // Now it is the human's turn again after the robot moved: the idle hint gate arms, so the hint
+    // button shows the 🔒 lock (it lifts after 30 idle minutes on a monotonic clock — not waited here).
+    await expect(page.locator('.lock')).toBeVisible();
+
     // Reload: the hash router restores the /game/<id> route and the local game replays from
     // IndexedDB with every committed tile intact.
     await page.reload();