Hidden Group and Hidden Group Membership

When "only necessary for grouping", you already have your excel, where they are grouped, right?
I am not kidding, when you don't need many of the default features of an AD or Entra ID group, then why not use a different group?
Your requirements can easily be fulfilled when you just manage the group in Excel, in a sharepoint list or in a database.

The question is, does this group need to be able do anything?
If e.g. the members of this group need to have access anywhere, then you could use your service account to run scripts for repeatedly check all the places, where the members should be granted access and ensure, only the group members are set there. 

Please be aware, that depending where you grant access, users can sometimes see, who else has access. 

To make it more weird and complex, just to fulfill the business requirement, you could create cyptic groups (e.g. named with just a guid), where each group has only one member of these group members and non members cannot see the members of these groups. 

After this, you can either grant all these cryptic groups directly the permissions, wherever the group members should be granted access, or if nesting is allowed, you can put these cryptic groups into a parent group, where you can then grant access to the parent group.

This is not the usual way, how to use groups, but maybe this fits in your requirements.