Does my BahnCard discount also apply to the City-Ticket?

No, the BahnCard discount is only granted on the price of the long-distance journey when booking a saver or super saver fare. The additional City-Ticket for the saver and super saver fare is not discounted, as it is not part of the fare. Instead, the price of the respective transport association is applied, so that this fee is ultimately paid to the association.

The City-Ticket is included free of charge in the flexible fare. DB bears the costs for this.