Yes, I am answering my own question!
In draw.io, I discovered it is now possible to draw tree diagramas, either with horizontal or vertical layouts. Even though they seem made out of basic shapes and connectors, new tree-specific menus were now available when such entities are selected. Those menu options help in editing the tree by selecting or addind parents, siblings or infants instead of manually adding and connecting shapes.
With those menus, I created a new horizontal tree yesterday. Today when I opened it, I wanted to add new siblings and sub-tree but I realied all the tree editing options were gone. The diagram only behaved like normal shapes connected together. For reference, the first illustration shows a new horizontal tree dragged from the drawer correctly handled as a tree.
What enables draw.io to distinguish between a bunch of shapes and a tree layout? Is it possible to convert a set of shapes appropriatly connected into a tree layout?