As per understanding, stated problem statement need some customization
on audience where you can create audiences in target based on groups
that you created in AEM and align experiences accordingly in the target
activity. When user logged into the site, on that time while sending
request to target via mbox or at, you can pass profile data[1] as
parameter. So Target can pull requested data and based on that serve the
experiences.
[1]:https://experienceleague.adobe.com/docs/target/using/implement-...