Earlier quoted context omitted.
I can only reply that west of Hamburg, Karte means any kind of card. Credit card is explicitly Kreditkarte. I also speak German fluenty, including partial knowledge of some dialects, and Swiss German. Since my last time in Berlin was 10 years ago, I'll have to take it.
Even in the local Ämtern? In my experience they're the worst offenders here. For example, Zahlungsmöglichkeiten on these two pages: [1] "Am Standort kann bar und mit girocard (mit PIN) (ehemals EC-Karte) bezahlt werden." This means nothing with Visa/Mastercard, period. Doesn't matter if you have a direct debit account or revolving credit. If you try to pay with eg an N26 Debit Mastercard, they say "Leider akzeptieren…
When Girokarte/EC-Karte are accepted, there is no guarantee that Kreditkarte are as well.