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/server/handlers_user.go

@@ -153,6 +153,20 @@ func (s *Server) handleEnqueue(c *gin.Context) {
 	c.JSON(http.StatusOK, dto)
 }
 
+// handleCancel removes the caller from the auto-match pool (and drops any pending
+// matched result), so a cancelled quick-match neither blocks a re-queue nor later
+// surfaces a robot-substituted game the player abandoned. It is idempotent: cancelling
+// when not queued is a no-op success.
+func (s *Server) handleCancel(c *gin.Context) {
+	uid, ok := userID(c)
+	if !ok {
+		abortBadRequest(c, "missing identity")
+		return
+	}
+	s.matchmaker.Cancel(c.Request.Context(), uid)
+	c.Status(http.StatusNoContent)
+}
+
 // handlePoll reports whether the caller has been paired since queueing.
 func (s *Server) handlePoll(c *gin.Context) {
 	uid, ok := userID(c)