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.

backend/internal/game/helpers_test.go

@@ -69,6 +69,29 @@ func TestHintsRemaining(t *testing.T) {
 	}
 }
 
+func TestHintUnlockLeftSeconds(t *testing.T) {
+	now := time.Now()
+	// A gated vs_ai game on the caller's turn, the robot having moved 10 min ago (turn started then).
+	gated := Game{VsAI: true, ToMove: 0, MoveCount: 2, TurnStartedAt: now.Add(-10 * time.Minute)}
+	cases := []struct {
+		name string
+		g    Game
+		seat int
+		want int
+	}{
+		{"non-vs_ai is open", Game{VsAI: false, ToMove: 0, MoveCount: 2, TurnStartedAt: now.Add(-10 * time.Minute)}, 0, 0},
+		{"not the caller's turn is open", gated, 1, 0},
+		{"human first move (no robot move) is open", Game{VsAI: true, ToMove: 0, MoveCount: 0, TurnStartedAt: now}, 0, 0},
+		{"robot moved 10 min ago leaves 20 min", gated, 0, 20 * 60},
+		{"robot moved past the window is open", Game{VsAI: true, ToMove: 0, MoveCount: 2, TurnStartedAt: now.Add(-40 * time.Minute)}, 0, 0},
+	}
+	for _, c := range cases {
+		if got := hintUnlockLeftSeconds(c.g, c.seat, now); got != c.want {
+			t.Errorf("%s: hintUnlockLeftSeconds = %d, want %d", c.name, got, c.want)
+		}
+	}
+}
+
 func TestAllowedTimeout(t *testing.T) {
 	if !allowedTimeout(24 * time.Hour) {
 		t.Error("24h must be allowed")