https://defence-industry-space.ec.europa.eu/eu-defence-indus...

There is a new military Schengen project to make troops and unified military documentation across whole EU.

Obviously there will need to be a registry of personnel there, so these people can be prevented to leave.

On the side you have SIS Schengen, where you can (already) have an active arrest warrant for desertion.

Nothing indicates that European Union is going to fight against such registries. It's even the opposite.