Answer given by Mr Reynders on behalf of the European Commission
The regulation 2021/953 of the European Parliament and of the Council on the EU Digital COVID Certificate is based on Article 21(2) of the Treaty on the Functioning of the European Union and aims to facilitate this right to free movement within the EU.
To ensure that non-vaccinated persons can also benefit from free movement, the regulation establishes an EU-wide framework for the issuance, verification and acceptance of not only vaccination certificates, but also of test and recovery certificates. It states clearly that vaccination is not a pre-condition for exercising free movement rights.
The domestic use of COVID-19 certificates for other purposes than facilitating free movement within the EU does not fall within the scope of the regulation. Member States may indeed use the EU Digital COVID Certificate for domestic purposes, but are required to provide for a legal basis in national law that must comply, among others, with data protection requirements.
In case a Member State establishes a national system of COVID-19 certificates for domestic purposes, it should ensure that the EU Digital COVID Certificate can also be used in that context. In this way, travelers going to another Member State do not have to obtain an additional national COVID-19 certificate to access e.g. bars or restaurants.
To help ensure that tests are affordable for all citizens, the Commission has put EUR 100 million at the disposal of Member States to provide for tests that qualify for the issuance of an EU Digital COVID certificate. However, it is important to note that decisions as to the pricing of tests fall within the competence of Member States.
-  http://data.europa.eu/eli/reg/2021/953/oj