A group only has 2 attributes. A list of entity ids and a friendly name if you gave it one.
An attribute for the whole group makes no sense as each thing in the group can be completely different and in a different state. And often, they will have overlapping attributes that conflict with each other.
Did you create a light group? Or a regular group?
Actually, I’m not sure it makes a difference. A light group does a few extra things with attributes, but I don’t think it exposes them to the attributes list in the group. It uses them to determine if any light is RGB it would provide a color picker, etc.
But I could be wrong.