Here is what I'd like to propose then:
The current "search dialog" (the one which supports Paste) has a two-state toggle button, for choosing search on "text" vs. "headers".
I can extend this to add a third state, "sender", with appropriate visual feedback (right now the icon changes, and there are help prompts).
So to search on "sender", one would 1) bring up search 2) enter a query 3) tap the button twice to take it to "search by sender" state 4) press submit.
And then separately from that we can discuss what should be done with the current "search all headers with a swipe command" - should there be a new one, or should it be left as is, considering the user can refine search from a search results view.
Let's not conflate these two parts but keep them in mind.
The proposal is actually for something very very similar to Samsung's search UI, but more compact, and it also leaves room for the list of suggestions (previous searches).