feat(image): preserve transparency for alpha images end to end

Skip WebP re-encoding for PNG/AVIF/BMP uploads and any bitmap that
actually contains alpha, tag transparency-capable canvas uploads with
the transparent-image tone, and detect alpha in merged layers so the
composed node keeps a transparent tone.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

server/internal/application/layer_merge.go

@@ -309,6 +309,7 @@ func (s *DesignService) composeMergedLayer(ctx context.Context, projectID string
 			drawTextLayer(canvas, node, bounds, scale)
 		}
 	}
+	hasTransparency := mergedLayerHasTransparency(canvas)
 
 	var output bytes.Buffer
 	if err := png.Encode(&output, canvas); err != nil {
@@ -338,6 +339,10 @@ func (s *DesignService) composeMergedLayer(ctx context.Context, projectID string
 	if title == "" {
 		title = "Merged Layer"
 	}
+	tone := "natural"
+	if hasTransparency {
+		tone = "transparent-image"
+	}
 	return design.Node{
 		ID:      newID(),
 		Type:    design.NodeTypeImage,
@@ -347,11 +352,25 @@ func (s *DesignService) composeMergedLayer(ctx context.Context, projectID string
 		Width:   bounds.Width,
 		Height:  bounds.Height,
 		Content: content,
-		Tone:    "natural",
+		Tone:    tone,
 		Status:  "success",
 	}, nil
 }
 
+func mergedLayerHasTransparency(img *image.NRGBA) bool {
+	bounds := img.Bounds()
+	for y := bounds.Min.Y; y < bounds.Max.Y; y++ {
+		offset := img.PixOffset(bounds.Min.X, y)
+		for x := bounds.Min.X; x < bounds.Max.X; x++ {
+			if img.Pix[offset+3] < 255 {
+				return true
+			}
+			offset += 4
+		}
+	}
+	return false
+}
+
 func boundsForLayerMerge(nodes []design.Node) layerMergeBounds {
 	left := math.Inf(1)
 	top := math.Inf(1)
@@ -446,8 +465,8 @@ func sampleLayerColor(src image.Image, srcBounds image.Rectangle, srcWidth int,
 	}
 	u = clampFloat(u, 0, 1)
 	v = clampFloat(v, 0, 1)
-	fx := u * float64(srcWidth-1)
-	fy := v * float64(srcHeight-1)
+	fx := clampFloat(u*float64(srcWidth)-0.5, 0, float64(srcWidth-1))
+	fy := clampFloat(v*float64(srcHeight)-0.5, 0, float64(srcHeight-1))
 	x0 := int(math.Floor(fx))
 	y0 := int(math.Floor(fy))
 	x1 := clampInt(x0+1, 0, srcWidth-1)