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The key part is:
Summer By the EU - The Commission will set up a digital infrastructure that would facilitate the authentication of the Digital
Green CertificatesBy the Member States - Introduce the necessary changes in their
national health records systemsThat's never happening in the next couple of months, not in order to create an EU-wide system for checking at entry points. Mind you they might just do it at ports and airports and assume if you are inside the EU on a land border, someone else checked you (works for Luxembourg)
That said, I don't know that the EU has even worked with the UK on it so it'd only be EU residents I guess even if it did work.
https://ec.europa.eu/info/live-work-travel-eu/coronavirus-response/safe-covid-19-vaccines-europeans/covid-19-digital-green-certificates_en