Wie realistisch (oder unrealistisch) ist diese Rechnung für 2024? Was mich wundert, ist, dass ich für 2023 auch genau den gleichen Betrag an Nachzahlung gezahlt habe – 604,6 € (das habe ich auf meinem Kontoauszug gesehen), aber leider kann ich den Brief nicht finden.

It is highly unrealistic if it is the exact same amount.

Ask your landlord for the documents, eg for the heating from Techem and the rest from the Hausverwaltung. He has to provide you a copy so that you can check it for yourself.

Maybe it was an honest mistake of opening the 2023 document and forgetting to update the numbers or just sending you the wrong version of the 2024 document unknowingly.
Or maybe there was some malice involved, but that is hard to proove plus not really relevant in the end.

If there was a mistake involved your landlord has to update the document based on the actual numbers for 2024. Which might be higher or lower, just saying.