In the default template (order_new.html / order_new_guest.html) I found the variable "payment_html" (Payment Details). In case of the payment method Bank Transfer Payment the value for this variable is generated from the field Configuration / Settings / Stores / Payment Methods / Bank Transfer Payment -> Instructions.
So I found a workaround by adding the additional info to this field. However, these are not only displayed in the email, but also by default in the checkout process.
