Stage 17 round 5 — backend/correctness bug fixes

- Resign on the opponent's turn: engine ResignSeat(seat) resigns a specific seat
  (not just toMove); game.Resign bypasses the turn check and forfeits the actor's seat.
- Quick-match cancel was a UI no-op (only stopped polling): add the full path
  (REST /lobby/cancel -> gateway lobby.cancel -> client) and clear the matchmaker's
  pending result on Cancel, so a cancelled search is dequeued (no 'already queued', no
  later robot-substituted game). NewGame dequeues on cancel and on abandon.
- Lobby win/loss: result.ts ranked by score, so a 0-0 resignation read as a win.
  The winner now takes rank 1 and the viewer is placed from rank 2 — matching the
  game-detail screen.
- Friend request to a robot: robots no longer block requests; the request stays
  pending and expires (friendRequestTTL), mirroring a human who ignores it.
- Nudge cooldown: ErrNudgeTooSoon now maps to a distinct nudge_too_soon code with a
  correct message; the chat nudge button disables during the hourly cooldown; the
  nudge note reads 'Waiting for your move!' (button keeps the Nudge action label).
Tests: engine/service off-turn resign, matchmaker cancel-clears-result, friend-to-robot
inttest, result.ts 0-0 resignation, nudge_too_soon mapping.

ui/src/game/Chat.svelte

@@ -51,7 +51,7 @@
       onkeydown={(e) => e.key === 'Enter' && send()}
     />
     <button class="iconbtn" onclick={send} disabled={busy} aria-label={t('chat.send')}>⬆️</button>
-    <button class="iconbtn" onclick={onnudge} disabled={busy || !canNudge} aria-label={t('chat.nudge')}>🛎️</button>
+    <button class="iconbtn" onclick={onnudge} disabled={busy || !canNudge} aria-label={t('chat.nudgeAction')}>🛎️</button>
   </div>
 </div>
 

ui/src/game/Game.svelte

@@ -89,6 +89,20 @@
   const isMyTurn = $derived(!!view && view.game.status === 'active' && view.game.toMove === view.seat);
   const gameOver = $derived(!!view && view.game.status !== 'active');
   const bagEmpty = $derived((view?.bagLen ?? 0) === 0);
+  // Nudge cooldown (one per hour per game, mirrored from the backend): the control is
+  // disabled for an hour after the player's own last nudge. nudgeTick re-evaluates it on a
+  // timer while the chat is open, so it re-enables without waiting for a new message.
+  const nudgeCooldownSecs = 3600;
+  let nudgeTick = $state(0);
+  const nudgeOnCooldown = $derived.by(() => {
+    void nudgeTick;
+    const mine = app.session?.userId ?? '';
+    const last = messages.reduce(
+      (mx, m) => (m.kind === 'nudge' && m.senderId === mine ? Math.max(mx, m.createdAtUnix) : mx),
+      0,
+    );
+    return last > 0 && Date.now() / 1000 - last < nudgeCooldownSecs;
+  });
 
   async function load() {
     try {
@@ -145,6 +159,13 @@
     else if (e.kind === 'nudge' && e.gameId === id && panel === 'chat') void loadChat();
   });
 
+  // Tick the nudge cooldown while the chat is open so the control re-enables on time.
+  $effect(() => {
+    if (panel !== 'chat') return;
+    const h = setInterval(() => (nudgeTick += 1), 20000);
+    return () => clearInterval(h);
+  });
+
   function isCoarse(): boolean {
     return typeof matchMedia !== 'undefined' && matchMedia('(pointer: coarse)').matches;
   }
@@ -708,7 +729,7 @@
 
 {#if panel === 'chat'}
   <Modal title={t('game.chat')} onclose={() => (panel = 'none')}>
-    <Chat {messages} myId={app.session?.userId ?? ''} {busy} canNudge={!isMyTurn} onsend={sendChat} onnudge={nudge} />
+    <Chat {messages} myId={app.session?.userId ?? ''} {busy} canNudge={!isMyTurn && !nudgeOnCooldown} onsend={sendChat} onnudge={nudge} />
   </Modal>
 {/if}