As a purchaser, do I incur costs for using SOFORT?

Just the opposite: more than 20% of merchants grant you a discount when you use SOFORT.
Furthermore, according to the 2012 study of online payment by the EHI Retail Institute, SOFORT is the online payment method with which merchants are least likely to charge a payment fee.

https://www.sofort.com/eng-GB/buyer/sb/how-sofort-banking-works/