Settings -> Give Project gives a list of user names but there is no way to give the project to a group. This would be nice, because it's a natural progression for a package to become more important over time, and make sense to be managed by a group.
No this is in purpose. You can add more maintainers to the package, user or groups and you can set the default assignee in bugzilla to be a group using https://pagure.io/releng/fedora-scm-requests but having groups be main admin is something that is too tight to the dist-git deployment that adding this logic into pagure itself bloats the code.
Thanks for your report though, it's always appreciated.
Metadata Update from @pingou: - Issue close_status updated to: Invalid