feat(hint): unify the vs_ai idle hint online + offline (server-enforced, monotonic)

Online vs_ai hints were broken: #207 made the vs_ai hint button always-enabled and
wallet-free (assuming all vs_ai = the offline idle-gate), but the backend still served
online vs_ai from the allowance/wallet, so over-clicking hit ErrNoHintsLeft -> a generic
error toast. Now online vs_ai uses the SAME idle-gate model as offline.

Backend: Hint() for a vs_ai game skips the allowance/wallet and increments no hints_used
(owner: vs_ai counts toward no hint statistic), and is idle-gated from the SERVER clock --
it returns ErrHintLocked (code hint_locked) until the robot's last move + 30 min, else
serves the top move. GameState/StateView expose hint_unlock_left_seconds (server-computed
seconds remaining; 0 for a human game / first move / not-your-turn). Pure helper
hintUnlockLeftSeconds unit-tested.

Wire: StateView gains hint_unlock_left_seconds (FlatBuffers, additive); pkg/wire + gateway
transcode carry it (round-trip test).

Client: the gate counts down from a MONOTONIC clock (performance.now()) anchored to the
source's seconds-left when it lands (on load from the view; to the full window when the
robot moves), so a client clock change cannot skew it and a relaunch re-reads a fresh
value. The vs_ai hint button (online + offline) shows the lock + toast; doHint handles the
hint_locked backstop by re-syncing. Replaces #207's absolute hintUnlockAtMs on the
wire/model/delta (the offline record keeps the absolute for persistence; the view exposes
seconds-left).

Docs FUNCTIONAL(+_ru)/ARCHITECTURE updated. Verified: go build/vet + game/server/transcode
tests (+ new hintUnlockLeftSeconds); ui check 0 / unit 490 / e2e 198 (one pre-existing
webkit offline flake) / app entry 114.2/115.

ui/src/lib/hints.test.ts

@@ -31,25 +31,19 @@ describe('hintsLeft', () => {
   });
 });
 
-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);
+describe('hintGateRemainingMs (the vs_ai idle-hint gate, monotonic)', () => {
+  it('is 0 when the gate is open — a null anchor (the human first move, or a non-gated game)', () => {
+    expect(hintGateRemainingMs(null, 60_000, 5000)).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('is the window remaining minus the monotonic time elapsed since the anchor', () => {
+    // anchored at mono 1000 with 60s left; 20s of monotonic time later -> 40s left.
+    expect(hintGateRemainingMs(1000, 60_000, 1000 + 20_000)).toBe(40_000);
   });
 
-  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);
+  it('is 0 once the elapsed monotonic time reaches (or passes) the window', () => {
+    expect(hintGateRemainingMs(1000, 60_000, 1000 + 60_000)).toBe(0);
+    expect(hintGateRemainingMs(1000, 60_000, 1000 + 90_000)).toBe(0);
   });
 });