Smart UV Project on multiple objects simultaneously, but independently? How do I perform Smart UV Project on multiple objects/groups/components simultaneously, but independently?

When I try, it creates one giant UV unwrap/map that combines everything into one.
You don't.

If you want to have independent UV maps for each of your mesh, you have to perform the Smart UV on each mesh separately. You cannot select everything, perform Smart UV and expect to have have independent UV maps for every thing that you selected. That's just not how it works.