[Lizard]

Perhaps it will help if you think of setting the project as setting the parent. So if you set the parent of an action that's already inside an action group, you're taking it out of that action group to put it under the project.
On the other hand, if you set the project of the action group, then the action group should become a child of the project, and the actions grouped under it should stay grouped under it when they all move to the project.
If that's not how it's behaving, I think that's a bug.