You could use the Run CLI Actions in Confluence add-on (which provides the ability, among other things, to get a list of groups and add members to groups) and the Run Self-Service Reports for Confluence add-on (which contains a Run macro that presents a form to a user to make selections, e.g., which group to join) to do what you describe.
The macros in both of these macros are "Macro Security Managed Macros", which means their use can be limited to only Administrators or other trusted users/groups.
Some examples of how to a self-service form can be found here.
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