... How to show that the emergency stop switch in the control cabinet does not belong to the press. There is approx. 2 metres distance to the maintenance hatch on the press.
A detailed statement can only be made when the situation on-site has been examined.
However, in general it is possible to say that in such a case, the plant operator must conduct a hazard assessment in accordance with the industrial safety regulations (BetrSichV). This will also consider the emergency stop.
It is highly likely that the emergency stop will not necessarily need to be interlinked. If there is a risk that confusion may arise, then the emergency stop should be marked accordingly, to prevent such confusion.
However, in the case described the workstation is probably not constantly in use and the area is only accessed for maintenance purposes, so this may not be necessary.