Codeberg allows private repositories: https://docs.codeberg.org/collaborating/repo-permissions/
If you do not want anyone (apart from your fellow collaborators) to see your repositories, mark your repository as "Private".
https://docs.codeberg.org/getting-started/first-repository/
Repositories are either public or private, where public means that everyone will be able to access your repository, while your private repositories can only be accessed by you and your collaborators (see Invite Collaborators).