Why is one of the lines / edges visible on my mirror All edges / phases have been created in the same way, by the extrusion tool. So I do not understand why one of them seems to be unique.
Can anyone help me understand what is happening here?
Here is my project file
If you (try to) select one of the triangles defined by the problematic edge, you will see that it's actually a quad:

So the edge there is not defining any face. Blender doesn't display edges defining faces in Object Mode, but it does display edges that don't define a face. In a way your problem proves the usefulness of this approach, as thanks to that, you noticed a problem with your topology.
You can simply select the edge and press X, then E to remove it. If you want to divide this quad into two triangles, then after removing current edge select appropriate vertices and press J to Join them. This will cut through the existing face like with a knife tool, instead of adding an edge on top of existing topology without changing it.