Not sure I am one who does understand, BUT it sounds like your are talking about layer sets in Chief not necessarily annotations sets. And yes, in Chief you can pre-select a layer set via a annotation set selection and assign that to a view.
AFAIK - Arch has nothing like that - they only have the layer combinations which only controls the view ability, not pre- assignment of layers to objects based on a view or layer combination. You have to use favorites to achieve that which is a extra step as are most things in Arch. However, even in Chief, they will not re-assign layers to existing objects. That is a manual process. So the only convenience in Chief is in the initial placement or use multi-select. In Arch you can pre-asign layers to the default but you can not assign defaults to a combination layer set. i believe that could be easily done through the API, but I doubt if you want to go there?
Unless, of course, I missed something?
Windows 10 - Visual Studio 2019; ArchiCAD 26