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/resign_test.go

@@ -69,6 +69,39 @@ func TestResignTrailingPlayerLoses(t *testing.T) {
 	}
 }
 
+// TestResignSeatOffTurn covers a forfeit on the opponent's turn: after player 0
+// moves it is player 1's turn, yet player 0 resigns its own seat — the resigner
+// loses, the opponent wins, and the game ends.
+func TestResignSeatOffTurn(t *testing.T) {
+	g := openingGame(t)
+
+	hint, ok := g.HintView()
+	if !ok {
+		t.Fatal("opening game has no hint")
+	}
+	if _, err := g.SubmitPlay(hint.Dir, hint.Tiles); err != nil { // player 0 moves
+		t.Fatalf("player 0 play: %v", err)
+	}
+	if g.ToMove() != 1 {
+		t.Fatalf("after player 0's move, toMove = %d, want 1", g.ToMove())
+	}
+
+	// Player 0 resigns although it is player 1's turn.
+	rec, err := g.ResignSeat(0)
+	if err != nil {
+		t.Fatalf("player 0 off-turn resign: %v", err)
+	}
+	if rec.Player != 0 || rec.Action != ActionResign {
+		t.Errorf("resign record = seat %d action %v, want seat 0 resign", rec.Player, rec.Action)
+	}
+	if !g.Over() || g.Reason() != EndResign {
+		t.Fatalf("game over=%v reason=%v, want over with resign", g.Over(), g.Reason())
+	}
+	if res := g.Result(); res.Winner != 1 {
+		t.Errorf("winner = %d, want 1 (the non-resigner)", res.Winner)
+	}
+}
+
 // TestResignOnFinishedGame rejects a second transition.
 func TestResignOnFinishedGame(t *testing.T) {
 	g := newEnglishGame(t, 1)