[lib] Fix thread search order for thick threads

Summary:
PERSONAL / PRIVATE should be ordered the same way in search results as GENESIS_PERSONAL / GENESIS_PRIVATE. This addresses ENG-9410.

Depends on D13531

Test Plan: Tested searching on both web and native

Reviewers: tomek, kamil, inka

Reviewed By: inka

Differential Revision: https://phab.comm.dev/D13532