Earlier quoted context omitted.
We took that train, realised when we got to the other end of the line that we hadn't gotten where we expected, then turned back to the place where it separates. Waited for the next advertised train to airport (it's signalled on the electronic board as two separate entries; yes, it says "board whatever carriages for airport, and the rest for ...", or at least I assume it did, as it was in German of course; but again,…
I've never had trouble buying train tickets with a credit card in Germany. If I had to guess, your issue was that you were trying to use a card that didn't support chip-and-PIN or contactless payments.
As opposed to... swiping the card?
Are there really cards out there that exclusively support that?