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/hints.test.ts

@@ -31,19 +31,25 @@ describe('hintsLeft', () => {
   });
 });
 
-describe('hintGateRemainingMs (the vs_ai idle-hint gate, monotonic)', () => {
-  it('is 0 when the gate is open — a null start (the human first move, or a non-gated game)', () => {
-    expect(hintGateRemainingMs(null, 5000, 1000)).toBe(0);
+describe('hintGateRemainingMs (the vs_ai idle-hint gate)', () => {
+  it('is 0 when the gate is open — no unlock time (the human first move, or a non-gated game)', () => {
+    expect(hintGateRemainingMs(undefined, 5000, 1000)).toBe(0);
+    expect(hintGateRemainingMs(0, 5000, 1000)).toBe(0);
   });
 
-  it('is 0 once the idle window has fully elapsed', () => {
-    expect(hintGateRemainingMs(0, 1000, 1000)).toBe(0);
-    expect(hintGateRemainingMs(0, 1500, 1000)).toBe(0);
+  it('is 0 once the unlock instant has passed (the gate is open)', () => {
+    expect(hintGateRemainingMs(1000, 1000, 1000)).toBe(0);
+    expect(hintGateRemainingMs(1000, 1500, 1000)).toBe(0);
   });
 
-  it('counts down the monotonic time remaining while still gated (only the delta matters)', () => {
-    expect(hintGateRemainingMs(0, 400, 1000)).toBe(600);
-    expect(hintGateRemainingMs(1000, 1400, 1000)).toBe(600);
+  it('is the wall-clock time remaining while still gated', () => {
+    expect(hintGateRemainingMs(1000, 400, 1000)).toBe(600);
+  });
+
+  it('clamps to the window, so a clock set back cannot freeze the gate above the window', () => {
+    // now shoved far into the past (device clock moved back): the raw remaining would exceed the
+    // window, but the cap keeps it at the window so the wait stays bounded and self-heals.
+    expect(hintGateRemainingMs(1000, -100_000, 1000)).toBe(1000);
   });
 });