search: move searcher-only logic to searcher package
Created by: rvantonder
Follow up of https://github.com/sourcegraph/sourcegraph/pull/30871.
As in title, plus minor renames to destutter and formatting for large number of arguments.
Context: I'm realizing I really want separate jobs for Zoekt
/Searcher
. It's still just extremely difficult to modify logic to optimize for any specific backend without being able to manipulate only that state/job.
Test plan
Just moving stuff around, already covered by tests.