It seems SQL Developer can only handle single files from the working copy of a Git repository.
Open a file (.pls, .sql...) from the working copy of Git repository (File -> Open...).
Use the context menu (right click within the file area/window on windows) to get the Git menu entries.
After that (and only after that) the Versions window will show the branches, remotes ...
Thanks, that was the trick! Open a file first.