Hi Kirk,
Oh duh!
That's a good question.
For me, if the Search Snapshot saved both the Searchable Fields and the search itself, I'd just save a blank search with the Searchable Fields set in some way and then save another with the Searchable Fields set in some other way and go from there. One fewer button.
Would that be confusing to other people? I have no idea.
I think I understand why the star icon. Was there a huge discussion about that?
I hope you're staying safe.
-Carl