I do agree the Berlin door is beefier than the Fichet Torinos and to my eyes the taper seems pretty steep which also suggests Parma. But the Parmas have a smaller rectangular pane in the middle while the Berlin door’s pane goes all the way to the outside edge, like the Fichets.
Here is an example of a Parma door:

The Berlin door seems to have elements of Parma (size and a steep taper) and Fichet (rectangular panel going all the way to the edge). And I think the Berlin ramp even looks like the Parma. So I’m not 100% convinced but now I’m leaning more towards agreeing that it’s a Parma.