Once you click on it, there is a confirmation dialog. Promoting this milestone will make this milestone available to all projects inside this group. Existing project milestones with the same name will be merged. Are you sure?
Once you confirm, you are navigated to the group milestone list page. E.g. https://gitlab.com/groups/gitlab-org/milestones. (This is different from the label promotion flow.) There is a banner across the top telling you that the promotion happened. Milestone was promoted to a Group Milestone
Out of scope
No changes to the visual design.
The dashboard, group, project milestone list views all remain the same. None of those are changing.