No, they probably don’t: HZ Kreditkartentest
According to HZ in May 2022 the overall cost was 4.1% (with the Mastercard), I would be surprised if the Amex then would be cheaper. But you do get the 1% cashback, so net would be 3.1%.
Otherwise I absolutely agree. The new Cumulus is not competitive for foreign transactions (and neither for domestic ones).
A surprise for me from the HZ test: Apparently the ZAK Visa Debit is also very good, 0.4% overall costs, compared to about 0.2% for Wise and bascially 0 for Revolut, Neon, Yapeal.