Where are you looking for the user groups to show up? Are the bases where you want to use the groups part of the Enterprise workspace? Does reloading Airtable / clearing cache help?
I find it easier to have a single permission level per group to limit the number of times I have to do one-off permission setting. I find the in general, people who are members of multiple groups have the highest permission level possible across all groups for a particular base. For example, if someone is part of a creator group and an editor group, the person is a creator.
You also need to make sure that your creators are careful when they share a base with someone. A creator can accidentally upgrade another user to creator levels when sharing.
