feat(ui): wire strip engine into UI auto-nest flow

When Strip is selected in the engine dropdown, RunAutoNest_Click
calls StripNestEngine.Nest() instead of sequential FillExact+Pack.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

OpenNest/Forms/MainForm.cs

@@ -785,8 +785,35 @@ namespace OpenNest.Forms
                     if (plate != activeForm.PlateView.Plate)
                         activeForm.LoadLastPlate();
 
-                    // Split items: Fill produces great results for qty > 1,
+                    var anyPlaced = false;
-                    // Pack is fast for single-quantity items.
+
+                    // Strip engine: use Nest() for multi-drawing strategy.
+                    if (NestEngineRegistry.Create(plate) is StripNestEngine)
+                    {
+                        var stripEngine = new StripNestEngine(plate);
+                        var stripParts = await Task.Run(() =>
+                            stripEngine.Nest(remaining, progress, token));
+
+                        activeForm.PlateView.ClearTemporaryParts();
+
+                        if (stripParts.Count > 0 && !token.IsCancellationRequested)
+                        {
+                            plate.Parts.AddRange(stripParts);
+                            activeForm.PlateView.Invalidate();
+                            anyPlaced = true;
+
+                            // Deduct placed quantities.
+                            foreach (var item in remaining)
+                            {
+                                var placed = stripParts.Count(p =>
+                                    p.BaseDrawing.Name == item.Drawing.Name);
+                                item.Quantity = System.Math.Max(0, item.Quantity - placed);
+                            }
+                        }
+                    }
+                    else
+                    {
+                        // Default: sequential Fill + Pack.
                         var fillItems = remaining
                             .Where(i => i.Quantity > 1)
                             .OrderBy(i => i.Priority)
@@ -798,7 +825,6 @@ namespace OpenNest.Forms
                             .ToList();
 
                         var workArea = plate.WorkArea();
-                    var anyPlaced = false;
 
                         // Phase 1: Fill each multi-quantity drawing with NestEngine.
                         foreach (var item in fillItems)
@@ -829,8 +855,6 @@ namespace OpenNest.Forms
 
                                 item.Quantity = System.Math.Max(0, item.Quantity - parts.Count);
 
-                            // Compute remainder within the current work area based on
-                            // what was just placed — not the full plate bounding box.
                                 var placedBox = parts.Cast<IBoundable>().GetBoundingBox();
                                 workArea = ComputeRemainderWithin(workArea, placedBox, plate.PartSpacing);
                             }
@@ -852,7 +876,6 @@ namespace OpenNest.Forms
                                 activeForm.PlateView.Invalidate();
                                 anyPlaced = true;
 
-                            // Deduct packed quantities.
                                 foreach (var item in packItems)
                                 {
                                     var placed = plate.Parts.Count(p =>
@@ -862,6 +885,7 @@ namespace OpenNest.Forms
                                 }
                             }
                         }
+                    }
 
                     if (!anyPlaced)
                         break;