See english pdf of the law

1. CONTEXT OF THE PROPOSAL
• Reasons for and objectives of the proposal

"The right of Union citizens to move and reside freely within the European Union, enshrined in
Article 21 of the Treaty on the Functioning of the European Union (TFEU), is one of the
Union’s most cherished achievements, and an important driver of its economy. At the same
time, the ongoing coronavirus disease 2019 (‘COVID‑19’) pandemic continues to pose an
extraordinary threat to public health across the Union. This has led Member States to adopt
public health measures seeking to protect individuals’ health as well as the capacity of their
healthcare systems, some of which have been related to travel between Member States"

"To facilitate safe free movement during the COVID-19 pandemic, the European Parliament
and the Council adopted, on 14 June 2021, Regulation (EU) 2021/9531 establishing the EU
Digital COVID Certificate framework for the issuance, verification and acceptance of
interoperable COVID-19 vaccination, test and recovery certificates2. Regulation (EU)
2021/953 facilitates free movement by providing citizens with interoperable and mutually
accepted certificates on COVID-19 vaccination, testing and recovery that they can use when
travelling. Where Member States waive certain restrictions on free movement for persons in
the possession of proof of vaccination, test or recovery, the EU Digital COVID Certificate
allows citizens to profit from these exemptions."

I think this depends per country on how far they want to control and genocide their citizens.