If all goes as planned, EU residents will not be legally allowed to enter another EU country as of July 1 without a covid passport. Article 45 of the EU Charter of Fundamental Rights guarantees the "right to move and reside freely within the territory of the Member States."
Under Art. 52, "limitations may be made only if they are necessary and genuinely meet
objectives of general interest recognized by the Union or the need to protect the rights and freedoms of others." Public health is a "general interest," yet the corona situation is improving so much that Czechs may now travel to Germany by vehicle without any covid requirement whatsoever. This normal state of affairs is to be abolished abruptly on July 1. There might indeed be a valid argument during times of heightened infection for limiting movement and requiring healthy people to have a covid passport, but doing so now accentuates the question of whether the EU still recognizes that its citizens have fundamental rights.