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/model.ts

@@ -82,10 +82,11 @@ export interface StateView {
   bagLen: number;
   hintsRemaining: number;
   walletBalance: number;
-  /** For a vs_ai game, the wall-clock ms at which the idle hint unlocks — persisted so the wait
-   *  survives a relaunch, and sanitised on read so a device clock set back cannot freeze it — or
-   *  0/undefined while open (the human's first move, or a non-vs_ai game). See lib/hints. */
-  hintUnlockAtMs?: number;
+  /** For a vs_ai game, the seconds until the idle hint unlocks (computed by the source: the SERVER
+   *  clock online, the device clock offline) — 0/undefined while open (the human's first move, or a
+   *  non-vs_ai game). The client anchors a MONOTONIC countdown (performance.now()) to it on receipt,
+   *  so a client clock change cannot skew it; a relaunch re-fetches a fresh value. See lib/hints. */
+  hintUnlockLeftSeconds?: number;
 }
 
 export interface MoveResult {
@@ -425,7 +426,7 @@ export interface GameList {
  */
 export type PushEvent =
   | { kind: 'your_turn'; gameId: string; deadlineUnix: number; opponentName: string; moveCount: number }
-  | { kind: 'opponent_moved'; gameId: string; move?: MoveRecord; game?: GameView; bagLen: number; hintUnlockAtMs?: number }
+  | { kind: 'opponent_moved'; gameId: string; move?: MoveRecord; game?: GameView; bagLen: number }
   | { kind: 'game_over'; gameId: string; result: string; scoreLine: string; game?: GameView }
   | { kind: 'chat_message'; message: ChatMessage }
   | { kind: 'nudge'; gameId: string; fromUserId: string; senderName: string }