Earlier quoted context omitted.
Where do you live in Europe? This has simply not been my experience at all in France, Germany, UK, Italy and Spain so far. Online shops most of all don’t take debit at all and bricks and mortar shops will accept credit more often than debit. Again, my experience. And I prefer to pay with debit because I know the shop will pay less fees. I get refused at Starbucks, random shops in train stations, etc.
Unless they have a direct agreement with a credit card company, most payment providers will give one-size-fits-all blended rate about 2.7% per transaction, even if it's debit.
I use a German bankcard and it will cost less to the merchant, that is the reason credit card were refused for such a long time. Covid broke this, as contactless was preferred and bankcard were not available for payment on smartphones at the time.