My understanding is that the responses are signed, but in a way that prevents linking signatures across vendors, so the same card being used for verification on different sites could not be linked, while the same card being used multiple times for the same vendor could.

As I'm not an expert on the crypto underlying the protocol, feel free to check the eIDAS standard for more info (the documents are in English, even if the link is not): https://www.bsi.bund.de/EN/Themen/Unternehmen-und-Organisati...