This feature is available in Enterprise and Ultimate editions.
I created a new backlog group for a project. Why isn't it listed in the backlog group drop-down menu when I edit stories/backlog items in the same project?
Backlog Groups are only available to the projects below the level at which it was created. If your new backlog group isn't listed in the backlog group drop-down list when you edit a backlog item, then the backlog group is probably in a sibling or child project. You can move the backlog group to a higher level project so that it will be available to stories in the current project level.
To move a backlog group in the project hierarchy:
Go to the Product > Backlog Groups page.
Select and edit the backlog group you'd like to move.
In the Project-Release field, check where the currently selected project is in the hierarchy.
Select a project with a higher level if necessary.