But cards are offline from the perspective of the consumer. Sometimes even on the merchant side of things. Not that it is an important distinction nowadays--but I have definitely tried to pay with a merchant's own app-based payment solution that refused to load due to a bad cellular connection. I haven't looked into how Wero will handle this.
Most payment terminal nowadays use 4g network and it is not uncommon to see shop/restaurants employees in some areas trying to desperately get a signal by moving the terminal close to the door or window.