I checked again with both Agoda & my bank and you are not correct they charged me in EUR.

Agoda uses different partners and state; “ Agoda’s rates come from our most updated, independent partners. As Agoda works with different partners, we are unable to share a specific source.” So it is Agoda (or their selected partner) who sets the very unfavourable exchange rate. Agoda refunded a part of the difference after my complaint.