R1:78b89711cbdd

Move a bunch more rendering into SearchEngine

Summary: Ref T4986. These are mostly mechanical now, I skipped a couple of slightly tricky ones. Still a bunch to go.

Test Plan:
For each engine:

- Viewed the application;
- created a panel to issue the query.

Reviewers: btrahan

Reviewed By: btrahan

Subscribers: epriestley

Maniphest Tasks: T4986

Differential Revision: https://secure.phabricator.com/D9017