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/inttest/game_test.go

@@ -299,6 +299,42 @@ func TestResignWinnerAndStats(t *testing.T) {
 	}
 }
 
+// TestResignOnOpponentTurn checks the Stage 17 fix: a player can forfeit on the
+// opponent's turn. Seat 0 plays (so it is seat 1's turn), then seat 0 resigns its own
+// seat while it is not its turn — no ErrNotYourTurn, the game ends, and seat 0 loses
+// despite leading on score.
+func TestResignOnOpponentTurn(t *testing.T) {
+	ctx := context.Background()
+	svc := newGameService()
+	seats := []uuid.UUID{provisionAccount(t), provisionAccount(t)}
+	seed := openingSeed(t)
+	g, err := svc.Create(ctx, game.CreateParams{
+		Variant: engine.VariantEnglish, Seats: seats, TurnTimeout: 24 * time.Hour, Seed: seed,
+	})
+	if err != nil {
+		t.Fatalf("create: %v", err)
+	}
+
+	hint, ok := newMirror(t, seed, 2).HintView()
+	if !ok {
+		t.Fatal("no opening move")
+	}
+	if _, err := svc.SubmitPlay(ctx, g.ID, seats[0], hint.Dir, hint.Tiles); err != nil { // p0 scores, now p1's turn
+		t.Fatalf("p0 play: %v", err)
+	}
+
+	res, err := svc.Resign(ctx, g.ID, seats[0]) // p0 resigns OFF turn
+	if err != nil {
+		t.Fatalf("off-turn resign = %v, want nil", err)
+	}
+	if res.Game.Status != game.StatusFinished || res.Game.EndReason != "resign" {
+		t.Fatalf("after off-turn resign: %+v", res.Game)
+	}
+	if res.Game.Seats[0].IsWinner || !res.Game.Seats[1].IsWinner {
+		t.Errorf("winner flags wrong (resigner must lose): %+v", res.Game.Seats)
+	}
+}
+
 // TestTimeoutSweep auto-resigns an overdue game and records it as a timeout.
 func TestTimeoutSweep(t *testing.T) {
 	ctx := context.Background()