Copy from multiple layers

You can select multiple objects in a diagram from different layers and move them around on the drawing canvas. This does not change what layer they 'live' on.

However, copying objects in a draw.io diagram does not copy their layer information. When you copy your selection to the clipboard (Ctrl+C) and paste it back onto the drawing canvas or into another diagram (Ctrl+V), all the copied objects will be pasted into a single layer.

Import a diagram file to import layer information

When you drag and drop a .drawio diagram file onto your drawing canvas, if that diagram had layers, these will be created and added to the Layers dialog, preserving the new shapes' layer structure.

So, when you want to preserve the layer structure of selected shapes and connectors, export your selection to an XML file, then import that file into your target diagram.