The "green certificate" concept the EU is proposing applies to intra-EU travel. And, it's not here yet. The EU site does provide the following about travel from non-EU countries.
"Could today's proposals also facilitate travelling to the EU from third countries?
At the moment, non-essential travel to the EU is restricted from third countries, except for a limited number of countries. A non-EU national who may travel to the EU can obtain a Digital Green Certificate. The non-EU national could request a Digital Green Certificate from a Member State he/she is travelling to, by providing all necessary information, including reliable proof of vaccination. The Member State would then have to assess if reliable proof has been provided and decide whether to issue a Digital Green Certificate.
In the medium-term, where the Commission is satisfied that a third country issues certificates in compliance with international standards and systems which are interoperable with the EU system, the Commission can issue an “adequacy decision” through an implementing act based on the regulation proposed today. Then, such third country certificates would be accepted under the same conditions as Digital Green Certificates.
In both cases, the rules for acceptance of proof of vaccination would be the same as for EU nationals: vaccines that have received EU-wide marketing authorisation have to be accepted, but Member States can decide to accept other vaccines in addition."
Sounds like many details and systems to be worked out yet.
The UK is not part of the EU any more, so don't know if the EU "green certificate" approach will be adopted by the UK.
Where is the US at on the concept of a vaccination passport/green certificate?
Here in Canada it seems that discussion has started but the "privacy" commissioners are already making noise about being careful with personal data. I don't see an approach and a supporting system being in use in the near future. In the meantime I have a piece of paper that says I got the first Moderna shot with a date for the second shot in July. I wonder if the EU would feel this is sufficient proof. Or, the UK? So many unknowns.