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.

backend/internal/engine/game.go

@@ -248,17 +248,29 @@ func (g *Game) Exchange(tiles []byte) (MoveRecord, error) {
 // winning regardless of score. A missed-turn timeout reuses Resign in the game
 // domain, so it inherits this win/loss.
 func (g *Game) Resign() (MoveRecord, error) {
+	return g.ResignSeat(g.toMove)
+}
+
+// ResignSeat resigns a specific seat regardless of whose turn it is, so a player
+// may forfeit on the opponent's turn. The resigning seat always loses (winner()
+// skips resigned seats). The turn cursor only advances when the seat that resigned
+// was the one to move; resigning an off-turn seat leaves the current player's turn
+// intact. It returns ErrGameOver on a finished game or for an out-of-range or
+// already-resigned seat.
+func (g *Game) ResignSeat(seat int) (MoveRecord, error) {
 	if g.over {
 		return MoveRecord{}, ErrGameOver
 	}
-	player := g.toMove
-	g.resigned[player] = true
-	g.disposeHand(player)
-	rec := MoveRecord{Player: player, Action: ActionResign, Total: g.scores[player]}
+	if seat < 0 || seat >= len(g.hands) || g.resigned[seat] {
+		return MoveRecord{}, ErrGameOver
+	}
+	g.resigned[seat] = true
+	g.disposeHand(seat)
+	rec := MoveRecord{Player: seat, Action: ActionResign, Total: g.scores[seat]}
 	g.log = append(g.log, rec)
 	if g.activeCount() <= 1 {
 		g.finish(EndResign)
-	} else {
+	} else if seat == g.toMove {
 		g.advance()
 	}
 	return rec, nil