Herewith an update. I just spoke to my bank and explained the problem. They then immediately blocked my credit card, stating that this is the only solution to at least prevent Newton from collecting money again. My bank will send me a completely new credit card free of charge within 5 working days.
In addition, my bank offers an online Money Back Service that I can use from 30 days after the transaction (which was last December 13 in my case) until 120 days after the transaction to receive at least the money back from this last transaction. I have to provide evidence for this, though, that I did my best to get in touch with Newton, and made multiple attempts. Fortunately, I still have all these (one-sided) emails and have also taken screenshots.
So, it looks like my bank will at least refund me the 50 USD from the most recent transaction. Unfortunately, that does not apply to the transaction from a year earlier.