If you get next to the cubes 1 and 2, interaction if offered, there is a popup window with ""F1" or "F2". If you press the "F" button, "OnInteracted()" is executed.
If you get even nearer to the cubes 1 and 2, "BeginOverlay()" works - The cube turns from white to green.
With the original project: If I get next to the cube 3, I neither see a "F3" popup window, nor is "BeginOverlay()" executed.
The only difference is in the hierarchy tree: there is one extra group / folder level above "cube 3". By that, somehow, the trigger function is not working.
I forgot to set collision on in the client contect !
After I did, the updated project worked fine.