Hello again Sanne,
Before going to the German pharmacy I e-mailed them the EU-doctor pdf-prescription, to ask if it was OK to use. So as Curious points out, perhaps you can try a different pharmacy (and email upfront)

Thanks for your answers Ken and Curious. But according to How prescriptions work in Sweden • E-hälsomyndigheten , the pharmacy acted correctly by not accepting my printed email-prescription as it is not supposed to be valid in Sweden:

Whether or not your prescription from another EU Member State is valid for dispensation in Sweden depends on whether it is an e-prescription or a paper prescription. In order for your prescription to be valid in Sweden, it must be a paper prescription for cross-border use, see information below for the minimum requirements of such a prescription.

EDIT: but funny that Curious was able to get a real paper prescription from EU doctor. When I contacted them and asked specifically about it, all they could offer was a printed version of an email-prescription.

Yes, first they mailed me paper prescriptions, which came to my house after a week or so. The PDF they sent to me looked exactly the same as the paper prescriptions, and the QR code on the printed PDF worked perfectly, just like the QR code on the prescriptions they sent to me by regular mail.